Frustration, Orbital Fluctuations, and Topology in Kondo Lattices and their relatives

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I shall discuss high magnetic field neutron scattering, thermomagnetic, and XMCD measurements probing the magnetism of the Kondo insulator SmB6 and its response to various dopants.

The de Haas-van Alphen effect, describing oscillations of the magnetization as a function of magnetic field, is commonly assumed to be a definite sign for the presence of a Fermi surface (FS) in a metal. Here we show that, in contrast to this canonical situation, there can be quantum oscillations even for insulators of certain types [1,2]. We draw connections to recent experiments on the topological Kondo insulator (TKI) candidate SmB$_6$ [1]. In addition, we show that TKIs are susceptible to the formation of bound electron-hole pairs [3]. These excitons can account for long-standing thermodynamic and recent transport anomalies in SmB$_6$ which is crucial for the identification of bulk topological signatures. References: 1. J. Knolle, N.R. Cooper, Phys. Rev. Lett. 115, 146401 (2015) 2. J. Knolle, N.R. Cooper, Phys. Rev. Lett. 118, 176801 (2017) 3. J. Knolle, N.R. Cooper, Phys. Rev. Lett. 118, 096604 (2017)

The definition of symmetry-protected topological (SPT) phases usually relies on a gap to bulk excitations and an unbroken symmetry. In this work, we show how topological protection of edge modes can also arise in gapless and symmetry-broken phases, as long as they are proximate to a gapped SPT phase. Our results rely on a decorated domain wall picture, which enabled us to write exactly-solvable models in one and two dimensions. Given the fact that a lot of candidate materials for spin liquid phases are found to be symmetry-broken at low temperature, this provides specific signatures to look for when trying to establish the presence of a proximate topological phase in the phase diagram.

The fate of the fermionic quasiparticles near a magnetic quantum phase transition (QPT) in heavy-fermion (HF) compounds has been controversial for many years. It is generally believed that this Kondo destruction is driven by the critical fluctuations near the QPT. A novel renormalization group treatment of the quantum interference of Kondo and RKKY couplings reveals, however, that the HF quasiparticles can be destroyed by the RKKY interaction even without critical fluctuations [1], with far reaching consequences for the QPT scenario: The lattice Kondo temperature, $T_K^*(y)$, is suppressed in a universal way by the dimensionless RKKY coupling $y$, with a discontinuous breakdown at a critical value $y=y_c$. This agrees quantitatively with STM spectroscopy on continuously tunable two-impurity Kondo systems [2]. We analyze in detail most recent time-resolved THz reflectometry experiments on the HF compound CeCu$_{6−x}$Au$_x$ across the QPT at $x=0.1$ [3]. The theoretical as well as the experimental findings point to a new quantum critical scenario, realized in CeCu$_{6−x}$Au$_x$, where the HF quasiparticles disintegrate in that their spectral weight vanishes continuously, but $T_K^*(y)$ remains finite. This is consistent with $ω/T$ scaling as an indicator for critical Kondo destruction. [1] A. Nejati, K. Ballmann, J. Kroha, PRL 118, 117204 (2017). [2] J. Bork, Y.-H. Zhang, L. Diekhöhner et al., Nature Phys. 7, 901 (2011). [3] Ch. Wetli, J. Kroha, K. Kliemt et al., arXiv:1703.04443.

At the turn of the 20th century, physicists faced an uncanny range of unsolved problems: simple questions, such as why hot objects change color, why matter is hard and why the sun keeps on shining, went unanswered. These problems heralded a new era of quantum physics. What was truly remarkable about discovery in this heroic era, was the intertwined nature of research in the lab and in the cosmos: solving superconductivity really did help answer why the sun keeps on shining, while looking at the stars provided clues as to why matter is hard. The challenges facing us today, epitomized by our failure to quantize gravity and the mysteries of dark matter and energy, are not just problems facing particle physics and astronomy, but problems that challenge physics to its core. What is perhaps less well known, is that physics in the lab and cosmos are just as intertwined today, as they were a hundred years ago. I will talk today about the less well-known dark matter challenges of the solid state, epitomized by the strange metals with linear resistivity that accompany high temperature superconductivity, the recent discovery of insulators with Fermi surfaces and quantum criticality - the solid-state version of a black hole in the phase diagram. The solution of these laboratory-scale problems fundamentally challenge our understanding of emergent quantum matter, and they are no less intertwined with their cosmological counterparts than they were a hundred years ago. I will highlight three Dark-Matter challenges that have arisen in heavy fermion physics[1-4], emphasizing their connections with other strongly correlated quantum materials and discussing some of our recent theoretical efforts to make progress on them: quantum criticality, hidden order and the possibility of new classes of broken symmetry outside the Hartree-Fock/BCS paradigm and topology [5]. [1] Piers Coleman, “Heavy Fermions and the Kondo Lattice, a 21st Century Perspective”, arXiv:1509.05769 (2015). [2] Joe Thompson and Zachary Fisk, “Progress in Heavy Fermion Superconductivity: Ce115 and other materials”, J. Phys. Soc. Jpn. 81, 011002 (2012). [3]Philipp Gegenwart, Qimiao Si and Frank Steglich, ”Quantum criticality in heavy-fermion metals”,Nature Physics 4, 186 - 197 (2008). [4] Maxim Dzero et al, “Topological Kondo Insulators”, arXiv 1506.05635, Ann. Rev. Cond. Matt. Phys., Volume 7:249-280 (2016). [5]B. S. Tan et. al, “Unconventional Fermi surface in an insulating state”, Science 349, 287-290 (2015).

A magnetic dipole is a source of magnetism, while an electric dipole and quadrupole are responsible for a charge current and an elasticity. Such fundamental degrees of freedoms of electrons in solids are described by multipoles in a comprehensive way. In general, there exist four kinds of fundamental multipoles under space-time inversion (E: electric, M: magnetic, ET: electric toroidal, MT: magnetic toroidal multipoles). However, microscopic multipoles are so far mainly discussed within single orbital and single atomic site, in which only E and M multipoles with even-parity under spatial inversion are activated. Recently, we generalize a concept of microscopic multipoles in two ways: (i) a cluster multipole in sub-lattice systems, where a specific alignment of magnetic/electric dipoles over multiple atomic sites can be regarded as a single cluster-multipole, and (ii) a hybrid multipole in the mixed orbital systems. With these extensions, all of four kinds of fundamental multipoles are activated. I will discuss about the concept of the generalized multipoles, and the corresponding cross-correlated responses under spontaneous ordering of the generalized multipoles.

We present our recent studies of experimental tests for a new magnetoelectric (ME) effect of "electric-current-induced magnetization" expected in antiferromagnetic (AF) metals. This phenomenon was theoretically predicted to occur when the global inversion symmetry of a system is spontaneously broken by the AF ordering, where the ordered state can be described as possessing a uniform component of odd-parity "augmented multipoles" typified by a toroidal moment [1, 2]. We have thus far investigated three AF metals, UNi4B, CeRh2Si2, and CeRu2Al10, and found that all of them show such the ME effect in their AF ordered states [3]. The obtained experimental results have confirmed that a uniform magnetization component can be induced by applying electric currents in certain types of AF metals, and its magnitude and direction are closely coupled with the magnetic structure. Though this feature is essentially consistent with the theoretical prediction, we have also found some inconsistencies that ΔM is induced in unexpected geometries of electric currents and reported magnetic structures. We will discuss the implications and interpretation of these findings. References: [1] S. Hayami, H. Kusunose, and Y. Motome, Phys. Rev. B 90, 024432 (2014). [2] S. Hayami, H. Kusunose, and Y. Motome, J. Phys. Soc. Jpn. 84, 064717 (2015). [3] H. Saito et al., J. Phys. Soc. Jpn. 87, 033702 (2018).

A promising approach to realize quantum spin liquids is to enhance the spin-space symmetry from usual $SU(2)$ to $SU(N)$. While the $SU(N)$ symmetry with a general $N$ is implemented in ultracold atoms using nuclear spin degrees of freedom, its realization in magnetic materials is challenging. Here we propose a new mechanism by which the $SU(4)$ symmetry emerges in the strong spin-orbit coupling limit. In d1 transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent hopping between the $J_{eff}=3/2$ quartets, which is apparently not $SU(4)$-symmetric. However, in the honeycomb structure, a gauge transformation maps the system to an $SU(4)$-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in $\alpha$-ZrCl$_3$, the low-energy effective model is the $SU(4)$ Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. Extensions to three-dimensional systems, and general constraints on the $SU(4)$-symmetric systems will be also discussed. Reference: M. G. Yamada, M. Oshikawa, and G. Jackeli, arxiv:1709.05252.

TBA

We will see that non-coplanar chiral orderings can naturally appear in frustrated Mott insulators, which are not deep inside the Mott regime. I will discuss different aspects of these magnetic orderings, including their effective field theory and their unusual charge dynamics. For this purpose, I will also introduce a general framework for computing dynamical properties of Mott insulators for arbitrary U/t and temperature T.

Implanted muons give a unique local perspective on magnets and superconductors [1]. By measuring the rotation of the implanted muon spin in the local magnetic field, which in turn results from the dipolar field arising from nearby magnetic moments, one can follow the magnetic order parameter as a function of temperature. If there are a range of muon sites the technique can provide information about the internal magnetic field distribution. Even above the magnetic transition temperature, the measured relaxation of the muon spin can provide information about magnetic fluctuations and spin dynamics. In superconductors the technique is particularly valuable because the measured internal field distribution can allow us to infer the pairing mechanism. In iron-based superconductors, for example, competition between magnetism and superconductivity can be studied very effectively with this technique. However, there is a fundamental limitation of this technique which comes from the lack of knowledge of the implantation site of the muon and the uncertainty about the muon's perturbation of its host. We have found that this problem can be addressed using electronic-structure calculations using a technique my group and the Parma group have developed which we call "DFT+μ", density functional theory with an included muon [2-3]. I will also describe some recent experiments by the Oxford group on various novel magnets and superconductors [4-7]. [1] S. J. Blundell, Contemp. Phys. 40, 175 (1999) [2] J. S. Möller, D. Ceresoli, T. Lancaster, N. Marzari, and S. J. Blundell, Phys. Rev. B 87, 121108(R) (2013) [3] F. Bernardini, P. Bonfà, S. Massidda, and R. De Renzi, Phys. Rev. B 87, 115148 (2013) [4] F. Lang, P. J. Baker, A. A. Haghighirad, Y. Li, D. Prabhakaran, R. Valentí and S. J. Blundell, Phys. Rev. B 94, 020407(R) (2016) [5] F. R. Foronda, F. Lang, J. S. Möller, T. Lancaster, A. T. Boothroyd, F. L. Pratt, S. R. Giblin, D. Prabhakaran and S. J. Blundell, Phys. Rev. Lett. 114, 017602 (2015) [6] H. Sun, D. N. Woodruff, S. J. Cassidy, G. M. Allcroft, S. J. Sedlmaier, A. L. Thompson, P. A. Bingham, S. D. Forder, S. Cartenet, N. Mary, S. Ramos, F. R. Foronda, B. H. Williams, X. Li, S. J. Blundell, and S. J. Clarke, Inorg. Chem. 54, 1958 (2015) [7] F. K. K. Kirschner, F. Flicker, A. Yacoby, N. Y. Yao, and S. J. Blundell, Phys. Rev. B 97, 140402(R) (2018)

I will discuss quantum ground state in frustrated spin system on the breathing pyrochlore lattice and explain how the ground state changes its character depending on the spin quantum number $S$. I derive a low-energy effective model for general $S$, and demonstrate that the case of $S=1/2$ is special. The symmetry of the effective model determines the dimer or tetramer type LRO in the spin singlet sector. I will also explain its implication in spin structure factor $S(k)$.

We consider mixed itinerant/localized systems where the coupling between the local moments and the conduction electrons is intrinsically frustrated. This frustration can then hinder the formation of a Kondo singlet and bring new non-trivial physics even in strong coupling limit. To explore this, we study a simple, tractable model where the local moments are Ising, and their interactions with the electrons are fully frustrated. Using theoretical arguments and direct numerical simulations, we find a rich phase diagram as a function of temperature and coupling strength. This includes a Fermi liquid phase and a partially ordered phase at intermediate temperatures that extends to strong-coupling. At low temperatures a complex stripe ordering, hosting one-dimensional electronic channels, emerges from the partially ordered phase. Finally, we speculate on the appearance of similar physics in more realistic models of the Kondo couplings.

Heavy fermion systems provide a prototype setting to study the kind of quantum phases and fluctuations that are created by strong correlations. I will discuss a global phase diagram of heavy fermion metals, with an emphasis on the role of magnetic frustration and related tuning parameters for the quantum fluctuations of the local moments [1,2,3]. This problem will be addressed based on a quantum non-linear sigma-model representation from the ordered side, as well as using an extended dynamical mean field approach from the paramagnetic side. In the presence of spin-orbit couplings, I will discuss how topologically nontrivial metallic phases such as the recently proposed Weyl-Kondo semimetal [4] will further enrich the global phase diagram. [1] C.-C. Liu, P. Goswami, and Q. Si, Phys. Rev. B 96, 125101 (2017); P. Goswami and Q. Si, Phys. Rev. B 95, 224438 (2017). [2] H.-H. Lai, E. M. Nica, W.-J. Hu, S.-S. Gong, and Q. Si, to appear (2018). [3] Q. Si, Physica B 378, 23 (2006); Phys. Status Solidi B 247, 476 (2010); J. H. Pixley, R. Yu and Q. Si, Phys. Rev. Lett. 113, 176402 (2014). [4] H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, PNAS 115, 93 (2018).

Kondo lattices have proven valuable model materials for the field of strongly correlated electron systems. For instance, they have been at the forefront in exploring quantum criticality and, relatedly, high-temperature superconductivity. Here I present our recent results on two new frontiers: orbital fluctuations and topology. Firstly, in the cubic heavy fermion metal Ce$_3$Pd$_{20}$Si$_6$, physics is governed by the 4-fold degenerate $\Gamma_8$ ground state of the Ce $4f$ wave function, and its interaction with the conduction electrons. We have demonstrated that sequential Kondo destruction occurs in this system under magnetic field tuning, at quantum critical points (QCPs) at the borders of antiferromagnetic and antiferrorquadrupolar order. While across the former QCP the spin undergoes a localization-delocalization transition, the same happens at the latter QCP to the orbital degree of freedom. Both lead to unconventional quantum criticality, such as linear-in-temperature electrical resistivity [1]. Secondly, we have demonstrated that the canonical Kondo insulator Ce$_3$Bi$_4$Pt$_3$ can be transformed into a Kondo semimetal Ce$_3$Bi$_4$Pd$_3$. The substitution series Ce$_3$Bi$_4$(Pt$_{1-x}$Pd$_x$)$_3$ is isostructural, isoelectronic, and isosize, but involves a considerable change in spin-orbit coupling when replacing the heavy $5d$ element Pt by the much lighter $4d$ element Pd [2]. The end compound Ce$_3$Bi$_4$Pd$_3$ shows thermodynamic characteristics [2] of a recently predicted Weyl-Kondo semimetal [3]. [1] V. Martelli, A. Cai, E.M. Nica, M. Taupin, A. Prokofiev, C.C. Liu, H.H. Lai, R. Yu, R. Küchler, A.M. Strydom, D. Geiger, J. Haenel, J. Larrea, Q. Si, S. Paschenar, Sequential localization and strange-metal behavior of a complex electron fluid, aXiv:1709.09376 [2] S. Dzsaber, L. Prochaska, A. Sidorenko, G. Eguchi, R. Svagera, M. Waas, A. Prokofiev, Q. Si, and S. Paschen, Phys. Rev. Lett. 118, 246601 (2017). [3] H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, Proc. Natl. Acad. Sci. U.S.A 115, 93 (2018). Support from the Austrian Science Fund (doctoral program W1243 and projects P29296-N27 and I2535-N27) is gratefully acknowledged.

Phase transition that breaks the space inversion symmetry with maintaining time reversal symmetry, i.e., parity breaking transition, is encountered in some compounds, as Cd$_2$Re$_2$O$_7$ and CsW$_2$O$_6$. In such cases, it is possible to identify order parameters by measuring lattice distortion, though it is very small. The phase transition of tetragonal URu$_2$Si$_2$ at 17 K shows no clear lattice distortion and no clear evidence that time reversal symmetry is broken. Furthermore, recent Ru-NQR and Si-NMR experiments suggest that there are no signs of breaking 4-hold rotational symmetry at Ru and U site. Nevertheless, there are two possible space groups remain to be compatible with this situation; \#87 (I4/m, $C_{4h}^5$) and \#126 ($P4/nnc$, $D_{4h}^5$). They correspond to the ferro hexadecapole ($xy(x^2-y^2)$) ordering and the antiferro dotriacontapole ($xyz(x^2-y^2)$) ordering, respectively. The quantum oscillation measurements tell us the first Brillouin zone is unchanged in the antiferro magnetic phase with $q=(0, 0, 1)$ under pressure, so antiferro dotriacontapole ordering is preferred. A dotriacontapole is an electric odd parity multipole, which can be realized by a combination with {\it 5f} and {\it 6d} electrons.

Heavy electron materials exhibit exotic patterns associated with the physics of entangled multipoles in metallic environments. Pr and U heavy fermion materials are of particular interest, as the non-Kramers character of their magnetic ions leads to new classes of dipolar, quadrupolar and octupolar multiplets; sometimes they lead to localized multipolar ground-states but they can also form new kinds of entangled states with the conduction electrons driving “hidden” forms of order that are not easily identified within conventional classification schemes. In this talk I’ll discuss three intriguing cases of hidden order in $URu_2Si_2$, $UBe_{13}$ and the family of 1-2-20 Pr heavy fermion compounds. Non-Kramers doublets have been proposed as the origin of exotic orderings in URu2Si2 and UBe13, but the effects of strong valence fluctuations mask the crystal field configurations, so the proposals remain controversial. The newly discovered 1-2-20 Pr compounds provide a new opportunity, as in these materials the presence of a dense array of non-magnetic non-Kramers doublets has been confirmed experimentally. The dramatic similarity between pressure-induced superconductivity in PrTi2Al20 and in $UBe_{13}$ suggests that the pairing in these two materials share a common mechanism. More generally I will discuss how this family of 1-2-20 Pr materials provides perspective on the older mysteries of hidden order in $URu_2Si_2$ and $UBe_{13}$.

In the past few years, it has been theoretically and/or experimentally shown that the correlated Weyl metals Mn3X (X=Ir, Sn and Ge) exhibit extremely large anomalous Hall effect [1,2,3,4,5], spin Hall effect [6], anomalous Nernst effect [7,8], and magneto-optical Kerr effect [9,10], which are usually observed in ferromagnets. In this talk, I will discuss the electronic structure of Mn3X and then introduce a new order parameter, which we call cluster multipole (CMP) moment. I will show that CMP characterizes the anomalous transverse transport in antiferromagnets with general spin configurations [11]. I will also discuss how CMP is useful for designing functional antiferromagnets. [1]H. Chen, Q. Niu, and A. MacDonald, Phys. Rev. Lett. 112, 017205 (2014). [2]J. Kuebler and C. Felser, Europhys. Lett. 108, 67001 (2014). [3]S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015). [4]N. Kiyohara et al., Phys. Rev. Applied 5, 064009 (2016). [5]A. K. Nayak et al., Sci. Adv. 2, e1501870 (2016). [6]W. Zhang, W. Han, S. H. Yang, Y. Sun, Y. Zhang, B. Yan and S. Parkin, Sci. Adv. 2 e1600759 (2016). [7]M. Ikhlas, T.Tomita, T. Koretsune, M.-T. Suzuki, D. Nishio-Hamane, R. Arita, Y. Otani, S. Nakatsuji, Nature Physics 13, 1085 (2017). [8]X. Li, L. Xu, L. Ding, J. Wang, M. Shen, X. Lu, Z. Zhu and K. Behnia, Phys. Rev. Lett. 119, 056601 (2017). [9]W. Feng et al., Phys. Rev. B 92, 144426 (2015). [10]T. Higo et al., Nature Photonicsvolume 12, 73 (2018). [11]M.-T. Suzuki, T. Koretsune, M. Ochi and R. Arita, Phys. Rev. B. 95, 094406 (2017).

Recently, as the first case in an antiferromagnet, Mn$_3$Sn is found to exhibit a large anomalous Hall effect, even at room temperature. [1] Usually, this anomalous Hall effect is known to be proportional to magnetization and thus has been observed only in ferromagnets. The spontaneous Hall resistivity in the antiferromagnet with vanishingly small magnetization indicates that the large fictitious field equivalent to a few hundred T must exist in the momentum space. [1, 2] Recent DFT calculation predicts that the large fictitious field may well come from a significantly enhanced Berry curvature associated with the formation of Weyl points nearby the Fermi energy $E_F$ . [3] Here, we report a striking discovery of a large spontaneous Nernst effect of ~ 0.35 $\mu$V/K in Mn$_3$Sn at room temperature and ~ 0.6 $\mu$V/K at low temperatures. The Nernst signals are found more than 100 times larger than what would be expected based on the magnetization. [4] Besides, we found strong experimental evidence of the Weyl fermions in Mn$_3$Sn, namely, that the band structure is found consistent with DFT by ARPES and the chiral anomaly is clarified in the magnetotransport measurements. Thus, our experiments demonstrate that the large anomalous Hall and Nernst signals arise from the Berry curvature associated with the Weyl points near the Fermi energy. [5] In our talk, we also propose that the large anomalous Hall and Nernst effects are useful for memory and thermopile devices, respectively. [1] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015). [2] N. Kiyohara, T. Tomita, and S. Nakatsuji, Phys. Rev. Applied 5, 064009 (2016). [3] H. Yang, Y. Sun, Y. Zhang, W-J. Shi, S. S. P. Parkin, and B. Yan, New Journal of Physics 19 (1), 015008 (2017). [4] M. Ikhlas, T. Tomita, T. Koretsune, M. –T. Suzuki, D. Nishio-Hamane, R. Arita, Y. Otani, and S. Nakatsuji. Nature Physics 13, 1085 (2017). [5] K. Kuroda, T. Tomita, M.-T. Suzuki, C. Bareille, A. A. Nugroho, P. Goswami, M. Ochi, M. Ikhlas, M. Nakayama, S. Akebi, R. Noguchi, R. Ishii, N. Inami, K. Ono, H. Kumigashira, A. Varykhalov, T. Muro, T. Koretsune, R. Arita, S. Shin, Takeshi Kondo, S. Nakatsuji, Nature Materials 16, 1090 (2017).

In the heavy-fermion metal CePdAl, long-range antiferromagnetic order coexists with geometric frustration of one-third of the Ce moments. At low temperatures, the Kondo effect tends to screen the frustrated moments. We use magnetic fields $B$ to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with $B$ employing thermodynamic probes such magnetization, specific heat, and thermal expansion. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppressed, theliberated moments tend to maximize the magnetic entropy and strongly enhance the frustration. Based on our experiments, this field range may be a promising candidate to search for a quantum spin liquid.

The strongly correlated $f$-electron physics can be well described by Doniach phase diagram. Namely, magnetic order induced by Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is suppressed by Kondo effect, resulting in the quantum phase transition to heavy fermi liquid. This Doniach picture can be revised in strongly correlated $quadrupole$ system since quadrupole Kondo effect induces the non-fermi liquid in the single impurity limit due to the over screening effect, known as two-channel Kondo effect [1]. To study such quadrupole physics, nonmagnetic $\Gamma_3$ state, which can be realized in the cubic crystalline electric field (CEF) for non-Kramers $f^2$ systems such as Pr-based compounds, is suitable due to the absence of a magnetic dipole moment. The cubic Pr$Tr_2$Al$_{20}$ ($Tr$ = Ti, V) is the first example of quadrupolar Kondo lattice system, in which both strong $c$-$f$ hybridization and nonmagnetic cubic $\Gamma_3$ CEF ground state are realized [2-5]. Ferro-quadrupole order is observed at $T_{\rm Q}=2.0$ K for PrTi$_2$Al$_{20}$. For PrV$_2$Al$_{20}$, double transition probably due to antiferro-type quadrupole order and octupole order is observed at $T_{Q}=0.75$ K and $T*=0.65$ K. Besides, superconductivity is found at $T_{\rm c}$ = 0.2 K and 0.05 K in the quadrupole ordered state of PrTi$_2$Al$_{20}$ and PrV$_2$Al$_{20}$, respectively [6, 7]. Large effective mass $m*/m_0 \sim$ 20 and 140 for PrTi$_2$Al$_{20}$ and PrV$_2$Al$_{20}$ indicates the heavy fermion superconductivity. Surprisingly, $T_{\rm c}$ and $m*$ are highly enhanced by applying the pressure [8]. In this presentation, I will review the basic properties of the Pr$Tr_2$Al$_{20}$ ($Tr$ = Ti, V) and discuss unique properties of the quadrupole Kondo system including the recent experiments. [1] D. L. Cox, Phys. Rev. Lett., {\bf 59}, 1240 (1987). [2] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn., {\bf 80}, 063701 (2011). [3] M. Koseki, Y. Nakanishi, K. Deto, G. Koseki, R. Kashiwazaki, F. Shichinomiya, M. Nakamura, M. Yoshizawa, A. Sakai, and S. Nakatsuji, J. Phys. Soc. Jpn., {\bf 80}, SA049, (2011). [4] T. J. Sato, S. Ibuka, Y. Nambu, T. Yamazaki, T. Hong, A. Sakai, and S. Nakatsuji, Phys. Rev. B, {\bf 86}, 184419 (2012). [5] M. Matsunami, M. Taguchi, A. Chainani, R. Eguchi, M. Oura, A. Sakai, S. Nakatsuji, and S. Shin, Phys. Rev. B, {\bf 84}, 193101 (2011). [6] A. Sakai, K. Kuga, and S. Nakatsuji, J. Phys. Soc. Jpn., {\bf 81}, 083702 (2012). [7] M. Tsujimoto, Y. Matsumoto, T. Tomita, A. Sakai, and S. Nakatsuji, Phys. Rev. Lett. {\bf 113}, 267001 (2014). [8] K. Matsubayashi, T. Tanaka, A. Sakai, S. Nakatsuji, Y. Kubo, and Y. Uwatoko, Phys. Rev. Lett., {\bf 109}, 187004 (2012).

Heavy fermion quantum criticality is one of the central issues to be solved in contemporary condensed matter physics. It has been recognized that the important examples are seen frequently in metals containing lanthanide atoms with the Frank-Kasper polyhedral type cage structure. They exhibit novel phenomena at low temperatures, like unconventional type of anomalous Hall effect, spin liquid like behaviour, non-Fermi liquid behaviour driven by the hybridization between conduction electrons and quadrupole (orbital) moments, and so on. It was found that correlation between conduction electrons and electronic quadrupole moments, in particular leads to fascinating materials properties. For the Pr-based systems, the $\Gamma$$_{3}$ non-Kramers crystalline-electric-field (CEF) doublet ground state is often realized in a Pr$^{3+}$ ion with a 4$\it{f}$$^{2}$ configuration under cubic crystalline symmetry. Thus, the Pr-based systems with non-Kramers doublet ground states are suitable for study of the quadrupolar quantum criticality. In $\Gamma$$_{3}$ non-Kramers systems, the local quadrupole moment derived from Pr ion can be scattered by conduction electrons via two equivalent scattering channel ($\it{O}$$_{20}$, $\it{O}$$_{22}$), and the channel frustration sometimes leads to the imperfect screening of the quadrupole moments. Quadrupolar order can be successfully investigated using ultrasonic measurements where elastic anomalies reveal ground state properties including orbital degrees of freedom or motif. We have investigated elastic properties of the Pr based cage compound PrV$_{2}$Al$_{20}$ (Tr : Ti, V) by means of ultrasonic measurements. PrV$_{2}$Al$_{20}$ has the cubic CeCr$_{2}$Zn$_{20}$-type structure with the space group $\it{F}$d$\bar{3}$m. Pr and V atoms form a diamond structure and a $\beta$-pyrochlore type partial sub-lattices, respectively. PrV_{2}Al_{20} exhibits quadrupolar ordering at $\it{T}$$_{Q}$ = 0.65 K and heavy fermion superconductor with $\it{T}$$_{c}$ = 50 mK at ambient pressure.[1 -2] Furthermore, additional ordering was recently discovered at 0.75 K. We have clearly observed elastic anomalies in the temperature dependence of principal elastic constants at the ordering temperatures of 0.65 K and 0.75 K.[3] Based on the experimental data, magnetic field vs temperature phase diagram was constructed for PrV$_{2}$Al$_{20}$. The obtained result provides an extended insight into the fundamentals of a quadrupolar ordering derived from the non-Kramers doublet $\Gamma$$_{3}$. Furthermore, a pronounced elastic softening toward low temperature is revived by applying a magnetic field in the temperature dependence of the elastic constant (C$_{11}$-C$_{12}$)/2, due to the non-Kramers doublet $\Gamma$$_{3}$, being degenerate in the order parameter space ($\it{O}$$_{20}$, $\it{O}$$_{22}$).[4] In this talk, we discuss the low temperature elastic property, and also the nature of the order parameter and some types of possible phases in PrV$_{2}$Al$_{20}$, including a commensurate-incommensurate transition for the quadrupolar moment. In addition, we report the discovery of a field-tuned quantum criticality based solely on the quadrupolar degrees of freedom through the evolution with magnetic fields of the heavy $\it{f}$-derived quasiparticles in PrV$_{2}$Al$_{20}$ probed by the ultrasonic measurement. $\bf References$ [1] K. Araki et al, J. Phys. Soc. Jpn. Conf. Proc. $\bf {3}$, 011093 (2014). [2] M. Tsujimoto et al, Phys. Rev. Lett.$\bf {113}$, 267001 (2014). [3] Y. Nakanishi et al, (in press) [4] Y. Nakanishi et al, (in preparation)

Chiral spin liquids are fruitfully viewed as analogues of fractional quantum Hall liquids, which descend from introducing interactions into flat band models that act like Landau levels. In recent work, we have shown that an alternative physical viewpoint is to consider CSLs as molten versions of non-coplanar magnets which may suggest an experimental search for such phases in the vicinity of such non-coplanar magnetically ordered states. Using exact-diagonalization, DMRG, and variational wavefunctions, we make the case for this connection in various 2D lattices.

In heavy fermions, many exotic phenomena coexist such as hidden order, unconventional metal and superconductivity. In particular, Pr based Kondo materials Pr(TM)2(Al,Zn)20 exhibit unique multipolar order and superconductivity. Motivated by recent experimental results, we will focus on the multipolar ordering of Pr$^{3+}$ and discuss possible phase transitions, in addition to the field effect. Then we will also discuss this system may support d+id superconductivity driven by quadrupolar order fluctuations.

PdCrO$_2$ crystallises in the delafossite structure in which triangular lattice planes of Pd are sandwiched between Cr-O octahedra with the Cr ions also triangular co-ordinated. Angle resolved photoemission experiments give strong evidence that the Cr layers are Mott insulating, and the Cr$^3+$ moments order below 40 K. In contrast, the Pd layers host nearly free electrons with dispersions similar to those seen in the non-magnetic metals PdCoO$_2$ and PtCoO$_2$. PdCrO$_2$ therefore provides a natural heterostructure between these two fundamentally different states. I will review what is known about the material and discuss the opportunities that it presents for the study of novel physics.

The superconducting pyrochlore oxide Cd2Re2O7 has drawn attention as the only superconductor (Tc = 1.0 K) that has been found in the family of α-pyrochlore oxides since its discovery in 2001. Moreover, it exhibits two characteristic structural transitions from the cubic pyrochlore structure, with the inversion symmetry broken at the first one at 200 K [J. Phys. Soc. Jpn. 87 (2018) 024702]. Recently, it has attracted increasing attention as a candidate spin-orbit coupled metal, in which specific Fermi liquid instability may lead to an odd-parity order with spontaneous inversion-symmetry breaking [L. Fu, Phys. Rev. Lett. 115 (2015) 026401] and parity-mixing superconductivity [V. Kozii and L. Fu: Phys. Rev. Lett. 115 (2015) 207002; Y. Wang et al., Phys. Rev. B 93 (2016) 134512]. I report on our recent experimental progress on the low-temperature phases of Cd2Re2O7 [J. Phys. Soc. Jpn. 87 (2018) 053702] and review the present understanding of the compound.

Since the proposal of the exactly solvable Kitaev model, quantum spin liquids have gained renewed interest from both theoretical and experimental perspectives during the past decade. One of the most interesting aspects in the research of Kitaev type spin liquids is the emergence of Majorana fermions as fractionalized excitations. Despite a lot of experimental efforts to materialize the Kitaev spin liquids and to identify exotic excitations, there still remain many issues to be clarified. In this talk, we will present our theoretical results for the experimentally-accessible fingerprints of Majorana fermions, in comparison with recent experimental data. We will discuss various thermodynamic properties, spin dynamics, and the effect of an applied magnetic field. We will also make a remark on our recent efforts to extend the candidate materials for the Kitaev spin liquids.

Rare-earth based triangular antiferromagnets provide a novel playground for frustrated magnetism and quantum spin liquid behavior of spin-orbit coupled moments. YbMgGaO4 features spin-orbit moments from a Kramers doublet, which remain fluctuating down to very low temperatures. We discuss thermodynamic, magnetic and inelastic neutron scattering experiments with particular emphasis on the effect of Mg2+ and Ga3+ site randomness [1]. We also present our recent results on two related systems in which structural randomness enables robust Ising spins in triangular [2] and zigzag chain configurations [3], respectively. Eventually, we also focus on the effect of geometrical frustration in non-oxide intermetallics, such as Kondo lattice metals [4]. [1] Y. Li et al., PRL 117, 097201 (2016)& PRL 118, 107202 (2017)& Nat. Commun. 8, 15814 (2017). [2] Y. Li, S. Bachus, Y. Tokiwa, A.A. Tsirlin, P. Gegenwart, arXiv:1804.00696. [3] Y. Li, S. Bachus, Y. Tokiwa, A.A. Tsirlin, P. Gegenwart, arXiv:1804.00687. [4] Y. Tokiwa et al. ,Sci. Adv. 1, e1500001 (2016), R. Küchler et al., PRB 96, 241110(R) (2017). Work in collaboration with Yuesheng Li, Alexander Tsirlin and Yoshi Tokiwa. We acknowledge support by the German Science Foundation (TRR 80 and SPP 1666) and the Alexander von Humboldt Foundation.

We study a layered three-dimensional heterostructure in which two types of Kondo insulators are stacked alternatingly. One of them is the topological Kondo insulator SmB$_6$ , the other one an isostructural Kondo insulator AB$_6$ , where A is a rare-earth element, e.g., Eu, Yb, or Ce. We find that if the latter orders ferromagnetically, the heterostructure generically becomes a magnetic Weyl Kondo semimetal, while antiferromagnetic order can yield a magnetic Dirac Kondo semimetal. We detail both scenarios with general symmetry considerations as well as concrete tight-binding calculations and show that type-I as well as type-II magnetic Weyl/Dirac Kondo semimetal phases are possible in these heterostructures. We furthermore include ab initio calculations for the magnetic Weyl Kondo case. Our results demonstrate that Kondo insulator heterostructures are a versatile platform for design of strongly correlated topological semimetals.

The coexistence of ferromagnetism and superconductivity is one of the most interesting topics in the correlated electron systems1. The microscopic coexistence is established in three uranium ferromagnets, UGe2, URhGe and UCoGe. The ordered moment of U atom is small, compared to the free ion value for 5f2 or 5f3, thus the 5f electrons are itinerant. The large internal field due to the ferromagnetism is not compatible with the superconductivity based on the spin-singlet state. Therefore the spin-triplet state is believed to be realized. Surprisingly the field-reentrant or reinforced superconductivity is observed with the extremely large upper critical field. The unusual superconducting behavior is due to the ferromagnetic fluctuations and Fermi surface instabilities under magnetic field. We review our recent studies on URhGe and UCoGe with fine tuning field angle, pressure, and uniaxial stress, focusing on the Fermi surface instabilities and field induced phenomena. This work was done in collaboration with G. Bastien, A. Gourgout, B. Wu, G. Knebel, A. Pourret, D. Braithwaite, J. P. Brison, A. Nakamura, S. Araki, Y. Tokunaga, A. Nikitin, A. de Visser and J. Flouquet.

We explore emergent quantum phases in the Kondo lattice model, where itinerant electrons are coupled to quantum spin liquid state of interacting local moments. First, we consider the quantum spin ice state on the pyrochlore lattice and show that the coupling to itinerant electrons leads to novel quantum critical behaviors. We discuss possible application of this result to Pr2Ir2O7. Second, the Kitaev spin liquid on the honeycomb lattice is coupled to itinerant electrons. It is shown that this naturally leads to the appearance of topological superconductivity.

Geometrically frustrated magnets often possess accidentally degenerate ground states at zero temperature. At low temperature, thermal fluctuations lift the accidental degeneracy and tend to stabilize ground states with maximal entropy. This phenomenon, known as “order by disorder”, underlines the fluctuation contribution to the free energy landscape in frustrated magnets. In this talk, I show that one can control such free energy landscape in a non-equilibrium setting. In a frustrated magnet with precessional dynamics, the system’s slow drift motion within the degenerate ground state manifold is governed by the fast modes out of the manifold. Exciting these fast modes generates a tuneable effective free energy landscape with minima located at thermodynamically unstable portions of the ground state manifold. I demonstrate this phenomenon on pyrochlore XY antiferromagnet and triangular XY antiferromagnet, where short magnetic field pulse and/or AC magnetic field are sufficient to induce such non-equilibrium landscape.

Fractionalized Fermi liquids (FL∗) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL∗ phases based on Kitaev's Z2 spin liquid. We characterize the FL∗ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find triplet superconducting phases which mask the quantum phase transition between fractionalized and conventional Fermi liquid phases. Their pairing structure is inherited from the Kitaev spin liquid, i.e., superconductivity is driven by Majorana glue

Chiral magnets often show interesting properties associated with their peculiar spin structures. A typical example is a chiral soliton lattice (CSL), which was found in monoaxial chiral magnetic conductors CrNb$_3$S$_6$ [1] and Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$ [2]. These compounds show a helimagnetic state at zero field, and turn into the CSL in a magnetic field perpendicular to the helical axis. As the magnetic field increases, the spatial period of the CSL increases, and finally the system relaxes into a forced ferromagnetic state. To understand the electronic and magnetic properties in the CSL, it is crucial to take into account itinerant electrons. Nevertheless, most of the previous theoretical studies were focused on localized spin models. In this study, we investigate a minimal itinerant electron model, a one-dimensional Kondo lattice model with the Dzyaloshinskii-Moriya interaction, by variational calculations for the ground state and by Monte Carlo simulations for finite temperature properties. We show that the model exhibits peculiar behavior in an applied field, which was not found in the localized spin models. In particular, we find that the spatial period of CSL can be locked at particular values dictated by the Fermi wave number [3]. This finding suggests the possibility of spontaneous formation of the CSL even at zero field. We also show that the system exhibits nonlinear negative magnetoresistance in the CSL, which is closely related to the soliton density [4]. [1] Y. Togawa $\it{et al.}, J. Phys. Soc. Jpn. \bf{85}, 112001 (2016). [2] T. Matsumura $\it{et al.}, J. Phys. Soc. Jpn. \bf{86}, 124702 (2017). [3] S. Okumura, Y. Kato, and Y. Motome, J. Phys. Soc. Jpn. \bf{87}, 033708 (2018). [4] S. Okumura, Y. Kato, and Y. Motome, J. Phys. Soc. Jpn. \bf{86}, 063701 (2017).

We uncover four new spin-charge ordered ground states in the strong coupling limit of the Kondo lattice model on triangular geometry. Two of the states at one-third electronic filling (n=1/3) consist of decorated ferromagnetic chains coupled antiferromagnetically with the neighboring chains. The third magnetic ground state is noncollinear, consisting of antiferromagnetic chains separated by a pair of canted ferromagnetic chains. An even more unusual magnetic ground state, a variant of the 120∘ Yafet-Kittel phase, is discovered at n=2/3. These magnetic orders are stabilized by opening a gap in the electronic spectrum: a "band effect". All the phases support modulations in the electronic charge density due to the presence of magnetically inequivalent sites. In particular, the charge ordering pattern found at n=2/3 is observed in various triangular lattice systems, such as, 2H-AgNiO2, 3R-AgNiO2 and NaxCoO2.

Kitaev's honeycomb model is a remarkable exactly solvable spin-1/2 model, consisting of bond dependent Ising interactions, and with a gapless quantum spin liquid ground state. Even more remarkably such interactions are actually realized in a number of spin-orbit entangled Mott insulators, alongside other more conventional interactions. Here, motivated by the recent surge in interest in the behaviour of these materials in a magnetic field, we map out the complete phase diagram of the pure Kitaev model in tilted magnetic fields. Besides the expected gapped quantum spin liquid at low fields and the trivial polarized state at high fields we report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless gauge field resulting in a dense continuum of low-energy states. We discuss its stability in the presence of perturbations, Heisenberg and off-diagonal symmetric exchange interactions, that naturally arise in spin-orbit entangled Mott insulators alongside Kitaev interactions.

The 93Nb nuclear magnetic response (NMR) and 181Ta nuclear quadrupole resonance (NQR) techniques have been utilized to investigate the microscopic magnetic properties of the Weyl semi-metals, single crystal of NbP and powder of TaP and TaAs. We made detailed measurements on the temperature dependences of line profiles, Kight Sift and the quadrpole friquency as well as nuclear relaxation rate (1/T1T), all of which gave us a characteristic features associated with the Weyl physics. As a typical example, we discuss the temperature dependence of 1/T1T in TaP. Here, one can immediately observe that there exists a characteristic temperature, T=30 K, where the relaxation process has a crossover from a high temperature T^2 behavior which is associated with the excitations in the nodal structure of Weyl points to the low temperature Korringa excitations for a parabolic bands with a weak temperature dependence. The band structure calculation of TaP tells us that besides the normal bands, two types of Weyl points appear. The first set of Weyl points, termed W1 and located at much lower energy (about 40 meV) than the E_F. The second set of Weyl points, W2, are slightly higher in energy (about 13 meV) than E_F [1]. From this band structure one can easily imagine that the conventional Korringa process is valid in well below temperature corresponding to the W2 energy, while increasing temperature excitations at the W2 Weyl nodes become progressively dominant. A construction of the total relaxation processes, including an anomalous orbital hyperfine coupling, is illustrated we have good agreement with the experimental result.

Our current focus is on emergent quantum phenomena when a spin system with a macroscopic degenerate ground state is coupled to fermions. For example, classically, frustration leads to a macroscopic degenerate ground state that violates the third law of thermodynamics. Turning on quantum effects is bound to generate exotic states of matter. We have recently developed a general framework to simulate Kondo coupled spin-fermion models that are free of the negative sign problem within the auxiliary field quantum Monte Carlo approach [1]. As a case study we will present results for a Kondo lattice model on the honeycomb lattice supplemented by frustrating couplings between localized spins. We will provide evidence that this coupling term generates so called partial Kondo screened states of matter, where Kondo screening becomes site dependent so as to alleviate frustration effects and the lattice rotation symmetry is broken nematically [1]. [1] T. Sato, F. F. Assaad, T. Grover, Phys. Rev. Lett. 120, 107201 (2018)

The reciprocal relation is a fundamental principle assured by the symmetry of the system. It is, however, violated when a certain symmetry is broken. Such violation of the reciprocity has attracted much interest from both fundamental physics and applications, e.g., a p-n junction. Nonreciprocity has also been studied for the propagation of spin waves in magnetic materials. The most pronounced example is the magnetostatic surface wave, the Damon-Eshbach mode, which propagates on a material surface only in one direction. Also in bulk magnets, the breaking of inversion symmetry gives rise to nonreciprocal propagation of spin waves, which has been experimentally observed in ferromagnets and very recently, a polar antiferromagnet. Since a spin wave can carry a spin current, these nonreciprocal effects would be useful for applications in spintronics as well as magnonic devices. Further investigations on nonreciprocal responses to various external fields are highly desired. In this presentation, we propose a nonreciprocal response of a spin current in magnetic insulators. Specifically, we consider the spin Seebeck effect, a magnetothermal phenomenon in which a temperature gradient causes a spin voltage. We show that a nonreciprocal spin current can be generated as a nonlinear response to a temperature gradient, in addition to a linear reciprocal one. Such nonreciprocity appears in a different manner depending on the symmetry of the system. In particular, we find that polar antiferromagnets, in which the spatial inversion symmetry is broken, exhibit spin rectification: one-way spin current generation irrespective of the direction of the temperature gradient. We also show that centrosymmetric systems can exhibit a different nonreciprocal spin current when magnetic order breaks the inversion symmetry. As the representatives for the two cases, we calculate the reciprocal and nonreciprocal spin Seebeck voltage for the polar antiferromagnet α-Cu2V2O7 and the honeycomb antiferromagnet MnPS3. We clarify their dependence on temperature, the magnetic field, and the direction of the temperature gradient. We also discuss how the formation of magnetic domains affect the spin current generation.

Some of the most exciting discoveries in strongly correlated systems in recent years are related to phases of matter that have a topological nature, often conveniently described as novel types of vacua that host emergent quasiparticle excitations. The quasiparticles and their underlying vacuum are heavily intertwined: the local correlations in the vacuum have an impact on the properties of the quasiparticles and, vice versa, the motion of the quasiparticles can change the nature of the underlying vacuum. Developing a theory based on this idea is generally a tall order, and the effects of such feedback mechanisms remain largely unexplored. In this talk we investigate this feedback mechanism in the context of spin ice materials. At the microscopic level, we argue that the spin dynamics originates from transverse components of the internal exchange and dipolar fields, and is characterised by two distinct spin flip rates determined by the surrounding spin configuration. This points at an entirely novel type of annealed dynamics in spin ice systems. The separation in rates can be remarkably large in quantum spin ice compounds. By studying the resulting spectral properties of the quasiparticle excitations, we are able to compute their contribution to the magnetic conductivity, in good agreement with experimental results.

Spin liquid is a very exotic state where spins fluctuate without showing any long-range order even at ultralow temperatures. Such spin liquid state can be realized in geometrically frustrated materials. For example, pyrochlore oxides are typical frustrated magnets and (classical) spin ice state with macroscopically degenerated 2-in 2-out configuration is realized in Dy2Ti2O7 [1]. On the other hand, if the magnetic element is replaced with the one with a smaller spin such as Pr, quantum fluctuation, which lifts the macroscopic degeneracy of the spin ice, should be taken into account. Pr2Zr2O7 and Pr2Ir2O7 are the candidates of such “quantum” spin ice materials. Pr2Ir2O7 is metallic material and exhibits anomalous hall effect without magnetic field or magnetization, suggesting the possibility of chiral spin liquid [2]. Besides, recent Angle-resolved photoemission spectroscopy (ARPES) measurement reveals that the Ir conduction band quadratically touches valence band forming a Fermi node [3]. This quadratic band touching can be the origin of the various topological phases such as Weyl semimetals, which can also give rise to the intrinsic anomalous hall effect. Compared to Pr2Ir2O7, insulating Pr2Zr2O7 allows us to study much simpler quantum spin ice physics due to the absence of the conduction electrons. Pinch points, which are indications of spin-ice correlation and magnetic monopoles, are observed in Pr2Zr2O7 by the neutron scattering experiment [4]. In addition, an anomaly is reported from the recent thermal conductivity measurement [5]. Thermal conductivity shows enhancement under 200mK, and also a peak around 80mK. Since there are no thermal carriers at such low temperature, the theoretically proposed new quasiparticle "photon" must be the carriers [6]. Pr 3+ is a non-Kramers ion, and reacts sensitively to the lattice strain hence thermal expansion and magnetostriction becomes crucial physical properties. We have observed the metamagnetic transition in both thermal expansion and magnetostriction, also magnetization. In this session, I will report the result of thermal expansion/magnetostriction at low temperature and its physical interpretations, using high quality single crystal of Pr2Zr2O7. [1] A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan, B.S.Shastry, Nature 399, 333-335 (1999) [2] Y. Machida, S. Nakatsuji, S. Onoda, T. Tayama, T. Sakakibara, Nature 463, 210 (2010) [3] T. Kondo, M. Nakayama, R. Chen, J. J. Ishikawa, E.-G. Moon, T. Yamamoto, Y. Ota, W. Malaeb, H. Kanai, Y. Nakashima, Y. Ishida, R. Yoshida, H. Yamamoto, M. Matsunami, S. Kimura, N. Inami, K. Ono, H. Kumigashira, S. Nakatsuji, L. Balents & S. Shin , Nature Communications 6, 10042 (2015) [4] K. Kimura, S. Nakatsuji, J-J. Wen, C. Broholm, M. B. Stone, E. Nishibori & H. Sawa,Nature Communications 4, 1934 (2013) [5] Y. Tokiwa, et al., APS March Meeting 2016 [6] O. Benton, O. Sikora, N. Shannon, Phys. Rev. B 86, 075154 (2012)

The Hamilonian of a quantum impurity coupled to a Luttinger Liquid describes a large number of physical systems. It consists of fermions that are left- and right-moving on a line and interacting among themselves via a density-density coupling while scattering off a quantum impurity. Such a system can be realized in many ways. The impurities I will consider will be either a local potential scattering center or quantum dot which are attached to the Luttinger liquid in various geometries – edge coupled, side coupled or body coupled. I will present exact solutions of the various systems by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. The consistency of the construction is established through a generalized Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe Ansatz equations are derived by means of the Off Diagonal Bethe Ansatz approach. I will derive the spectra of the models for all coupling constant regimes and will calculate the impurity free energy. The high and low energy behavior of the system for both repulsive and attractive interactions will be discussed in detail. Among other things I will show that at low energies the quantum dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry. Although remaining strongly coupled for all values of the interaction in the Luttinger liquid, there exists competition between the tunneling and the backscattering leading to non Fermi liquid exponents in the specific heat and capacitance of the dot.

Particle-antiparticle production in the presence of a static classical electric field, known as the Schwinger mechanism, represents a central physical phenomenon in gauge theories. How the particle production is affected in the quantum limit, where the backaction onto the electric field becomes essential, remains a major challenge. In this work, we study particle-antiparticle production in the quantum quench dynamics after a strong coupling of the bare particles to dynamical gauge field in a 1D U(1) quantum link model(QLM). We find that for a strong coupling the system experiences dynamical quantum phase transitions (DQPTs) where the vacuum persistence probability (Loschmidt echo) develops non-analytic behavior at critical times. As opposed to the Schwinger mechanism, where matter fields are suddenly coupled to a classical electric field, we observe that the dynamics of the vacuum persistence probability and therefore the DQPTs cannot be understood using the classical picture of particle production. Instead, a quantum dynamical pattern emerges from the strongly coupled matter fields and dynamical gauge fields. In addition to the 1D system, we extend the study to 2D U(1) QLM without matter field. We also observe the quantum dynamics of the electric field develope DQPT when we quench to a different vacuum. We discuss how these findings are related and related possible experiments in quantum simulators such as trapped ions.

TBC

We discuss Kondo effect in the framework of a general model, describing a quantum impurity with degenerate energy levels interacting with a gas of itinerant electrons and derive scaling equation for the interaction parameters to the second order for such a model. The approach is applied to the spin-anisotropic Kondo model generalized for the case of the power law DOS for itinerant electrons. The scaling equation is specified and solved analytically in terms of elliptic functions. We also introduce spin-anisotropic Coqblin--Schrieffer model, apply the general method to derive scaling equation for that model and integrate the derived equation analytically.