korrel15: list of talks

When two magnetic impurities interact, this is usually described in terms of a competition between the Kondo effect and the Ruderman- Kittel-Kasuya-Yosida (RKKY) interaction (ref ). RKKY is an indirect exchange interaction which is mediated by the conduction electrons. De- pending on distance, it favours ferromagnetic or antiferromagnetic alignments of local moments, whereas the Kondo effect tends to quench the moments locally with the help of the conduction electrons. Here we describe a different scenario, in which the competition between the kinetic energy gain due to Kondo scattering and the bind- ing energy gain due to chemical interaction be- tween its constituents is the driving force of a quantum phase transition in a molecular dimer on a metal surface. Interestingly, in this sce- nario the Kondo effect favours the alignment of local moments, while the chemical interaction promotes the local quenching of the moments within the dimer. We expect this mechanism to be generic and widespread, because it relies only on very general features of chemical interactions and Kondo physics. Moreover, since it is straightfor- ward to engineer the chemistry, the mechanism will allow for an easy tuning of the magnetic in- teraction between local moments.

An important feature in Fe-based superconductors is that superconductivity occurs in the vicinity of nematic ordering — a lowering of the rotational symmetry preserving time-reversal invariance — as well as of magnetic order [1]. The origin of the nematic symmetry breaking has been heavily debated, because lattice, orbital, and spin degrees of freedom are all directly linked one another from a symmetry point of view, and thus it is challenging to establish which ordering is primary.  In this talk, I will present nuclear magnetic resonance (NMR) studies of the high-quality FeSe single crystals, demonstrating that orbital degrees of freedom drives the nematic order [2]. Our study also shows that nematicity not only competes with superconductivity [2], but also causes in-plane anisotropy of superconductivity in FeSe [3]. 

[1] R. Fernandes et al., Nature Physics 10,  97 (2014) 
[2] S.-H. Baek et al., Nature Materials 14, 210 (2015)
[3] S.-H. Baek et al., (unpublished, in preparation)

The question whether Anderson insulators can persist to finite-strength interactions - a scenario dubbed many-body localization (MBL) - has recently received a great deal of interest. We formulate a precise notion of a many-body localized state, and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of our definition; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. This yields a powerful numerical way of analyzing putative MBL phases. We show that there are systems that fall under this definition of many-body localization, and discuss the possibility of rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.

The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions. With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. 

In the past years, much progress has been made for certain spin, bosonic, and even fermionic quantum many-body systems. However, a large class of interacting models is thought to be exempt from numerical studies due to the fermion sign problem. At its heart, it occurs when the statistical weights in the simulation are positive and negative resulting in an exponential scaling of the algorithm instead of a polynomial one. In this work, we study the connection of the sign problem and the entanglement entropy using Determinantal Quantum Monte Carlo, the method of choice for unbiased, large-scale simulations of fermionic systems. We show that there is a strong correlation between the behavior of the entanglement entropy and the sign problem and that the particular structure of the ‘observable’ entanglement entropy to some extent allows to handle the sign problem much better than for usual correlation functions.

We investigate excitations of the low-energy j=1/2 system stabilized by spin-orbit coupling in square-lattice iridates. Both excitations within the j=1/2 states as well as between j=1/2 and j=3/2 states support the interpretation as a spin-orbit-assisted Mott insulator. The former excitations reveal the impact of Hund's rule coupling (or lack thereof). The j=3/2 excitations gives access to crystal field splitting and reveals a sharp quasi-particle-like peak. Even though the spin-orbit excitation is charge neutral, this feature is strongly reminiscent of that related to a hole in a Mott insulator. We argue that this similarity arises due to a mapping between the two situations, while the quasi-particle peak is not clearly visible in in ARPES performed on undoped Mott insulators, precisely the charge neutrality is argued to assist its detection in the present scenario. 

The emergence of new properties from low-dimensional building blocks is a universal theme in different areas in physics.  The investigation of transitions between isolated and coupled low-dimensional systems promises to reveal new phenomena and exotic phases.  In this talk we will consider two prototypical systems which show quantum phase transitions between a low-dimensional phase and higher dimensional behavior.  Interacting 1D bosons which are coupled in a two-dimensional array are maybe the most fundamental example of a system which illustrates the concept of a dimensional phase transition.  However, recent experiments using ultracold gases have shown a surprising discrepancy between theory and experiment [1] and it is far from obvious if the powerlaws from the underlying 1D theory can predict the transition temperature and order parameter correctly for all interaction strength.  A second system which has recently been debated in the literature is the J-J' Heisenberg antiferromagnet on the triangular lattice.  By tuning the ratio of J/J', both the dimensionality and the frustration are changed at the same time and it is still unclear if this system may have a spin-liquid phase or incommensurate order.  By using large scale numerical simulations (2D DMRG and 3D quantum Monte Carlo) we are able to study the phase transitions in great detail.  For the frustrated systems a simple analytical description of the phase transition can be obtained in terms of topological string excitations. This leads to an incommensutrate phase, but the excitations become unstable in a narrow region, which allow for a possible spin liquid phase.

[1] A. Vogler, R. Labouvie, G. Barontini, S. Eggert, V. Guarrera, and H. Ott 
Dimensional phase transition from an array of 1D Luttinger liquids to a 3D Bose-Einstein condensate, Phys. Rev. Lett. 113, 215301 (2014)

Exploiting the entanglement concept within a matrix-product-state based infinite density-matrix renormalization group approach, we show that the spin-density-wave and bond-order-wave ground states of the one-dimensional half-filled extended Hubbard model give way to a symmetry-protected topological Haldane state in case an additional alternating ferromagnetic spin interaction is added. In the Haldane insulator the lowest entanglement level features a characteristic twofold degeneracy. Increasing the ratio between nearest-neighbor and local Coulomb interaction V/U, the enhancement of the entanglement entropy, the variation of the charge, spin and neutral gaps, and the dynamical spin/density response signal a quantum phase transition to a charge-ordered state. Below a critical point, which belongs to the universality class of the tricritical Ising model with central charge 7/10, the model is critical with c=1/2 along the transition line. Above this point, the transition between the Haldane insulator and charge-density-wave phases becomes first order. 

Reference:
Florian Lange, Satoshi Ejima, Holger Fehske, arXiv:1506.04003.

Noninteracting particles in a random potential can form an Anderson localized state where single-particle wavefunctions are localized in some region of space.  The question how interactions affect such a state has recently attracted much interest, and theoretical progress has been made by looking at new dynamical observables.

In my talk I will review localization in many-body systems and show how a purification method can be used to perform exact binary disorder averages and substantially speed up DMRG-type quench simulations [1]. I give an outlook how one-dimensional lattice models with binary disorder can potentially be realized with two species of atoms, and how purification can be implemented also experimentally.

[1] F. Andraschko, T. Enss, and J. Sirker, Purification and many-body localization in cold atomic gases, Phys. Rev. Lett. 113, 217201 (2014).

Doped correlated electron systems may show various types of charge ordering interacting with the magnetic degrees of freedom, such as the stripes in the high-temperature superconductors. It has been shown [1] that regular magnetic lattices can be induced by the ordering of the residual magnetic moments within a charged ordered state. It is in particular possible to generate a Honeycomb lattice within the charged ordered state of the t-U-V Hubbard model of a triangular lattice close to 2/3 filling. This happens within the (110) state, where two out of three sites are singly-occupied, carrying a magnetic moment, with the third site being empty.

In the present work we consider the t-U-V Hubbard model on a Honeycomb lattice at 1/2 and 3/2 fillings and show that triangular lattices, which are characterized by residual anti- and ferro-magnetic interactions respectively, may be induced. In this case every second site is empty (for n=1/2), or doubly occupied (for n=3/2), and singly occupied respectively. We propose, that this approach can be used quite generally to generate interesting effective lattice structures, possibly with non-conventional magnetic interactions.

The hierarchical quantum master equation technique is a promising method to describe nonequilibrium impurity problems. It employs a hybridization expansion of the time evolution of the impurities density matrix from a product initial state. Using an advanced and systematic truncation scheme, convergence can be achieved if the temperature of the environment is not too low. Thus, numerically exact results can be obtained. This is corroborated by a direct comparison with the continuous-time quantum Monte Carlo approach. In particular, the nonequilibrium dynamics of interacting quantum dot systems is studied that can be described by Anderson impurity models. Thereby, the focus is on effects and phenomena that emerge on long time scales such as, for example, the steady-state magnetization or the complex build-up of coherences. 

The nature of the spin liquid ground state of the kagome Heisenberg model and the corresponding materials remains a big unsolved question in the condensed matter physics. Here, I will introduce the progress we have made on this problem by studying an extended kagome model with XXZ anisotropy.  Numerically (by DMRG), we find that the emergence of the spin-liquid phase is independent of the anisotropy of the XXZ interaction. The two spin liquid phases, a chiral and a time-reversal invariant spin liquid in the Heisenberg limit, exist even when an extremely strong easy-axis anisotropy is turned on. Theoretically, we focus on the easy axis limit which admits a faithful lattice gauge description. The dual lattice gauge model is  described by a compact U(1) gauge field coupled with bosonic spinons. Interestingly, we find that in this lattice gauge description,  the underlying physical mechanism of the chiral spin liquid is described by "gauging" a symmetry protected topological phase. This is a rare example that the spin liquid phase in a realistic model can be analyzed in a controlled way,  which opens a new avenue to study spin liquid physics in physical system.

[1] Yin-Chen He, Subhro Bhattacharjee, Frank Pollmann, and R. Moessner (to be submitted)
[2] Yin-Chen He, Subhro Bhattacharjee, R. Moessner, and Frank Pollmann, arXiv:1506.01645
[3] Yin-Chen He and Yan Chen, PRL 114, 037201 (2015).
[4] Yin-Chen He, D. N. Sheng and Yan Chen, PRL  112, 137202 (2014).

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase,
while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the  many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

One of the most intriguing phenomena in strongly correlated systems is the fractionalization of quantum numbers — familiar examples include the spin-charge separation in one-dimensional metallic systems, the fractionalization of the electron in fractional quantum Hall states or the emergence of monopoles in spin ice.

In this talk, I will discuss the fractionalization of magnetic moments in a certain class of Mott insulators, in which the emergent degrees of freedom are Majorana fermions that form an (almost) conventional metal. The origin of such a dichotomous state is elucidated by a family of exactly solvable models of frustrated quantum magnets in three dimensions, which might be realized in a class of recently synthesized Iridate compounds. These models thereby provide the first analytical tractable examples of long sought-after quantum spin liquids with a spinon Fermi surface and even an entire new class of quantum spin liquids — a so-called Weyl spin liquid, in which the fractionalized degrees of freedom form a topological semi-metal.

We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with SU(2) Gross-Neveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition. 

We analyze the scaling theory of two-dimensional metallic electron systems in the presence of critical bosonic fluctuations with small wave vectors, which are either due to a U(1) gauge field, or generated by an Ising nematic quantum critical point. The one-loop dynamical exponent z=3 of these critical systems was shown previously to be robust up to three-loop order. We show that the cancellations preventing anomalous contributions to z at three-loop order have special reasons, such that anomalous dynamical scaling emerges at four-loop order.

We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over 104 samples for lattices as large as 105 sites. We identify regimes in which non-ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.

Sr2IrO4  is a prototypical spin-orbital Mott insulator which has attracted considerable interest in recent years. Using electron spin resonance (ESR) measurements at sub-THz frequencies in strong magnetic fields we were able to untangle the 5d-shell electronic structure of Sr2IrO4, in particular, the exact order of the Ir t2g levels (for details, see [1]). To do that, we have experimentally determined the spectroscopic g-tensor which appears inverted as compared to predictions of canonical ligand-field theory. The inversion of the g-tensor implies an inversion of the ordering of the t2g orbital states. This has been confirmed on the quantitative level by ab initio quantum chemistry methods which yielded experimentally observed g-factors.  We show that in the layered structure of Sr2IrO4 a specific distribution of ionic charges between the IrO2 and SrO layers modifies the sequence of energy levels within the t2g and eg manifolds and consequently very fundamental physical properties such as the magnetic g-factors, which determine the relation between the magnetic moment and quantum number of a magnetic particle.

[1] Bogdanov, N. A. et al. , Nat. Commun. 6:7306 doi: 10.1038/ncomms8306 (2015).

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on mean-field for describing the real-time quantum dynamics of generic spin-1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting two-particle irreducible (2PI) effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures, and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the non-equilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states [S. Hild, et al. Phys. Rev. Lett. 113, 147205 (2014)]. 

The conditions for breakdown of Kondo quasiparticles near a heavy-fermion quantum phase transition are still a controversial issue. We present a renormalization group (RG) theory for the breakdown of Kondo screening in multi-impurity Kondo systems without direct interimpurity dipole coupling, without pre-assumptions about magnetic ordering or Fermi surface criticality. Kondo singlet formation is signalled by the RG divergence of the conduction electron-local Kondo spin vertex Γ at the Kondo scale TK. In a multi-impurity system, Γ acquires a non-local, RKKY-mediated contribution from conduction electrons scattering at surrounding Kondo sites, which depends on the dynamical, local spin response χ on those sites. Because of its inverse dependence on TK at low energies, χ = (gμB)2/TK, the β-function depends parametrically on the Kondo scale in a selfconsistent way. As a result, we find a universal suppression of the Kondo scale TK(y) in Kondo lattice and multi-impurity systems, depending on a dimensionless RKKY coupling parameter y. Local Kondo screening is predicted to break down at a maximum RKKY coupling ymax, where ymax is a universal function of the bare TK(0). At the breakdown point, the TK-suppression assumes the universal value TK(ymax)/TK(0)=1/e≈0.368, in remarkable quantitative agreement with STM spectroscopy on two-impurity systems [1]. 

[1] J. Bork et al., Nature Physics 7, 901 (2011).

A series of investigations of the Hubbard and the Hubbard-Heisenberg model with SU(N) symmetry in the self-adjoint representation have shown that complex valence bond solid (VBS) phases can emerge from simple, local interactions. The Hubbard model on the square lattice presents a particularly special scenario: The log2 instability towards magnetic order due to the density of state of the square lattice is dominant enough to induce weak, but robust AFM order in the weak coupling regime, even at SU(6). In the strong coupling regime the ground state is a four-fold degenerate plaquette VBS. We provide correlation ratios of the two distinct order parameters, from quantum Monte Carlo simulations, which vanish at the same point. This direct Néel-VBS transition is conjectured to be in the class of deconfined quantum criticality. We compare the universal functional form of the correlation ratios with results from the designer spin Hamiltonians.

Raman scattering investigations have been performed on different classes of topological materials ranging from topological insulators, Weyl/Dirac semimetals, AF insulators dominated by strong spin orbit coupling and Skyrmion lattice systems. There is evidence for a joint motif in the sense of resonant scattering to electronic states with strong spin orbit coupling as well as unusual selection rules of the observed phonon and electronic modes. We will review the present experimental status and compare it with available theoretical scenarios and modeling. 

The frequency-dependent optical conductivity σ(ω) of interacting graphene is determined within a full tight-binding lattice approach that avoids the divergences present in previous nodal Dirac approximation calculations. Our work confirms previous Dirac theory results that implement high-energy cutoff schemes which obey the Ward identity of charge conservation to regularize the divergences. Tight-binding and Dirac theory calculations are shown to agree even when the non-zero size of the atomic orbital wave function is included, conclusively demonstrating that σ(ω) is completely universal and uniquely determined by the low energy properties near the nodes of graphene.

I will present recent developments for flexible matrix product state (MPS) approaches to calculate finite-temperature spectral functions of low-dimensional strongly correlated quantum systems. The main focus will be on the determination of these quantities directly in frequency space via a Liouvillian formulation of the resolvent, wich combines the purification of the finite-temperature density operator with a moment expansion of the spectral functions of interest. The resulting algorithm does not specifically depend on the MPS formulation, but is applicable for any wave function based approach which can provide the purification of the density matrix, opening the way for further developments of numerical methods. Here, I will discuss its accuracy and efficiency for a specific MPS based formulation. More specifically, I will show results for finite-temperature properties of dynamical spectral functions of various spin chains, in particular systems with Dzyaloshinskii- Moriya interactions caused by spin-orbit coupling under the influence of magnetic fields, and dimerized chains. The goal is to analyze the effect of the symmetry breaking interactions on the nature of the finite-temperature dynamic spin structure factor as obtained in ESR and neutron scattering experiments.  

While the understanding of fractionalized topological phases has impressively developed in two dimensions (2D), much less is known in three dimensions (3D). In this talk, I present a 3D system of coupled quantum wires that exhibits fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems, and discuss that the coupled-wire approach provides a new, and powerful tool for the analysis of interacting topological physics in 3D.

In the array of wires considered in this talk, the coupled wire approach allows to identify the protected edge states associated with the topologically non-trivial bulk gapped phases. It also shows that these phases are separated by exotic quantum phase transitions corresponding to a rearrangement of fractional quantum Hall edge modes. Also an extended exotic critical phase may exist. Without electron-electron interactions, similar but unfractionalized bulk gapped phases based on coupled integer quantum Hall states exist. They are separated by an extended critical Weyl semimetal phase.

The investigation of interacting many-particle systems out of equilibrium has recently attracted a lot of attention. Yet the use of nonequilibrium scenarios for the numerical representation of ground state and excited state many-body wavefunctions is still a rather new aspect in the development of new numerical methods for correlated many-particle systems. However, first observations show that such approaches can provide viable and promising routes.

Full Configuration-Interaction Quantum Monte Carlo (FCIQMC) is such a wavefunction based numerically exact method and has been developed for electronic structure calculations in correlated many-electron systems. It both goes beyond the fixed node approximation and circumvents the sign problem present in other QMC treatments e.g. of the Hubbard model away from half filling. FCIQMC becomes a powerful method in the initiator approximation (i-FCIQMC) which, while being exact in a well-defined limit, inserts nonlinear and nonequilibrium aspects to an FCIQMC calculation.

After an introduction to i-FCIQMC calculations, numerically exact results for the Hubbard model away from half filling will be presented and compared with alternative approaches.

We will present synthesis strategies to access model compounds for the study of certain structure-property relationships.  Here we will focus on the AAg2M[VO4]2 family of magnetic compounds as examples for triangular and honeycomb lattices.  The aspect of geometrical frustration will be discussed in terms of space group symmetry for different spin-systems and charges of the magnetic ions.  In this context neutron diffraction studies and thermodynamic properties will be presented.  Additionally, we show that interesting scenarios in 2 D can be established through competing AFM and FM interactions.
References:
1 N.E. Amuneke, J. Tapp, C. deLaCruz, A. Möller, Experimental Realization of a Unique Class of Compounds: XY-Antiferromagnetic Triangular Lattices, KAg2Fe[VO4]2 and RbAg2Fe[VO4]2, with Ferroelectric Ground States, Chem. Mater. 26, 5930 (2014).
2 M. Bratsch, A.P. Litvinchuk, J. Tapp, A. Möller; Synthesis, Thermodynamic and Spectroscopic Properties of Honeycomb-Type Lattices: AAg2(M’1/3M2/3)[VO4]2; Inorg. Chem. 53, 4994 (2014).

The quantum kinetic equation for SU(2) symmetric systems is derived with special consideration of spin-orbit coupling in magnetic and electric fields. The theory is applicable for linear and nonlinear intrinsic and extrinsic spin-orbit coupling as well as graphene. The RPA response functions to an electric field are derived for arbitrary magnetic fields and spin-orbit coupling. The coupled density and spin response functions allow to describe dynamical classical, quantum, and anomalous Hall effect as well as spin-Hall effects and its inverse. The collective modes show a splitting due to polarization and/or spin-orbit coupling for neutral impurity scattering. The long-range Coulomb potential of charged impurities are considered and the spin-orbit coupling leads to characteristic modifications of the screening parameter. New high-frequency modes out-of-plane are found [7].

Spin-orbit coupling fit into the scenario of nonlocal kinetic theory which unifies the achievements of transport in dense gases with the quantum transport of dense Fermi systems [1,2,7]. The quasiparticle drift of Landau's equation is connected with a dissipation governed by a nonlocal and non-instant corrections to the collision integral expressed in terms of shifts in space and time [3]. Compared to the Boltzmann- equation, the presented form of virial corrections only slightly increases the numerical demands in implementations [4]. The balance equations for the density, momentum and energy include quasiparticle contributions and the correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy [5,6]. 

[1] V. Špička, P. Lipavský, K. Morawetz, Phys. Rev. B. 55, 5084 (1997); 5095 (1997)
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[7] K. Morawetz, Europhysics Letters, 104 (2013) 27005

The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured, that the tensor networks which arise during the real space renormalization procedure like the multi-scale-renormalization-ansatz (MERA) are discretized version of the background of the gravity theory. We strive to contribute to make this conjecture testable by considering an explicit and tractable example, namely the dual network of the toric code, for which MERA can be performed analytically. We examine how this construction can be extended to include excited states. Furthermore, we show how to calculate topological entanglement entropy from the geometry of MERA.

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Renyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. In this talk I will show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, I will present an efficient tensor network algorithm based on Projected Entangled Pair States (PEPS) to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Renyi entropies, this approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. Moreover, I will show how the method also allows the identification of Minimally Entangled States (MES), thus providing a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

Ref: F. Parisen Toldin, M. Hohenadler, F. F. Assaad, I. F. Herbut, "Fermionic quantum criticality in honeycomb and π-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo", Phys. Rev. B 91, 165108 (2015)

We present the phase diagram of the interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by recent experiments using laser assisted-tunneling in optical lattices [1] and lattices in synthetic dimensions [2], which studied the regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we explore the parameter space and calculate experimentally accessible observables.

For hardcore bosons, the phase diagram comprises gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes [3]. For moderate interactions, vortex lattices form at certain commensurate vortex densities. We also find the so-called 'biased leg phase', which shows density-imbalance between the two legs [4].

Very interestingly, an enlarged unit cell forms in the vortex lattice phases, which can lead to the reversal of the current circulation-direction. We demonstrate this effect for arbitrarily weak interactions and at sufficiently low temperature, and show that it is significant for intermediate interactions [5].

[1] Atala etal., Nature Phys. 10, 588 (2014)
[2] Mancini etal., arXiv:1502.02495
[3] Piraud etal., PRB 91, 140406(R) (2015)
[4] Wei and Mueller, PRA 89, 063617 (2014)
[5] Greschner etal., arXiv:1504.06564

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group (iDMRG) method based on the matrix-product state (MPS) representation of FQH states on an infinite cylinder. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T-transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder. Using these novel techniques, we provide numerical evidence for the existence of Fibonacci anyons in the 12/5 plateaux. 

The investigation of the ground state of the quantum antiferromagnet on the kagome lattice is one of the most challenging problems in the field of frustrated quantum magnetism. Over many years numerous theoretical methods has been applied to understand the ground-state properties of the kagome antiferromagnet (KAFM). While it became clear very early that ground-state magnetic long-range order (LRO) is absent for the  s=1/2 Heisenberg KAFM, there was a longstanding debate on the nature of the non-magnetic quantum ground state. Recent large-scale numerics provide strong arguments for a gapped  spin-liquid ground state for spin s=1/2. Since higher spin $s$ as well as anisotropy Δ, in general, lead to a reduction of quantum fluctuations,  ground-state magnetic LRO for the KAFM might be facilitated. Both, anisotropy as well as  higher spin, have also relevance for the experimental research. Moreover, anisotropic spin models are of great interest with respect to engineering models of quantum magnetism on optical lattices.
In my contribution I discuss the  ground-state phase diagram of the easy-plane XXZ kagome antiferromagnet for arbitrary spin quantum number s, i.e. the anisotropy parameter Δ varies between Δ=1 (isotropic Heisenberg model) and Δ=0 (XY model).
To calculate the ground-state phases we used the coupled cluster method at high orders of approximation. The interplay of frustration, quantum fluctuations and anisotropy  leads to a rich ground-state phase diagram with various ground-state phases.For the extreme quantum case, s=1/2, the ground state is magnetically disordered in the entire region 0 < Δ < 1. Quite  unexpectedly, the selection of the ground state by quantum fluctuations is different  for small Δ (XY limit) and for Δ close to one (Heisenberg limit).
For s=1 the ground state is disordered for 0.818 < Δ < 1, it exhibits √3x√3 magnetic LRO for 0.281 < Δ < 0.818, and q=0 LRO for 0 < Δ < Δc=0.281.
For larger spin s>1 the ground state is ordered in the entire region 0 < Δ < 1, where q=0 magnetic LRO is favored over √3x√3 LRO for 0 < Δ < Δc and vice versa for Δc < Δ < 1. We calculate the critical Δc as a function of the spin quantum number s.

Literature:
[1] O. Götze, D.J.J. Farnell, R.F. Bishop,  P.H.Y. Li, and J. Richter, Phys. Rev. B {bf 84}, 224428 (2011).
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For half-filled Hubbard model it is known {sl a priori} that antiferromagnetic fluctuations strongly affect the low energy physics from critical exponents[1] to the electronic self-energy at low temperatures[2]. In more a general situation, however, it is usually unknown which types of excitations are responsible for specificfeatures in the one-particle spectrum. Here, we demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems[3]. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. 
Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions out of half filling. In the latter case, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.

[1] G. Rohringer, A. Toschi, A. Katanin, and K. Held, Phys. Rev. Lett. 107,  256402 (2011).
[2] T. Schäfer, F. Geles, D. Rost, G. Rohringer, E. Arrigoni, K. Held, N. Blümer, M. Aichhorn, and A. Toschi, Phys. Rev. B 91, 125109 (2015).
[3] O. Gunnarsson, T. Schäfer, J. P. F. LeBlanc, E. Gull, J. Merino, G. Sangiovanni, G. Rohringer, and A. Toschi,Phys. Rev. Lett. 114, 236402 (2015).

In strongly spin-orbit coupled three-dimensional systems, spin liquids can form which are characterized by Majorana excitations with Fermi surfaces. Here we show that such systems generically dimerize at low temperatures in an exotic version of the spin-Peierls transition [1] and form a spin liquid with line nodes.
Our study builds on an analysis of Kitaev models weakly perturbed by, e.g., Heisenberg interactions. The dimerization transition is closely related to the BCS instability of fermions. In the presence of an external magnetic field, also incommensurate phases form, closely related to FFLO states predicted for superconductors.

[1] Maria Hermanns, Simon Trebst, Achim Rosch, preprint, arXiv:1506.01379 

We present 23Na - and 19F NMR results on the magnetically frustrated  XY -Pyrochlore NaCaCo2F7 with a frustration index of f=θCW/Tf≈56. 23Na NMR -spectra reveal the presence of two magnetically non equivalent Na sites in conjunction with the local Co2+ spin structure. Below ˜3.6 K both the 23Na - and 19F spectra broaden due to the formation of static spin correlations. A huge reduction of the 19F - and 23Na NMR signal intensity hints at a spin-glass/quasi-static field distribution in NaCaCo2F7. The 19F spin-lattice relaxation rate 19(1/T1) exhibits a peak at around ∼3 K, at the same temperature range where ac and dc susceptibility data show a broad maximum. The overall temperature dependence of 19(1/T1) can be described by the BPP theory considering a fluctuating hyperfine field with an autocorrelation function. The correlation time of the autocorrelation function exhibits an activation behavior further indicating the spin-glass state/spin-frozen state in NaCaCo2F7.

We study the effect of interactions on Kitaev's toy model for Majorana wires. We demonstrate that even though strong repulsive interaction eventually drive the system into a Mott insulating state the competition between the (trivial) band-insulator and the (trivial) Mott insulator leads to an interjacent topological insulating state for arbitrary strong interactions. We show that the exact ground states can be obtained analytically even in the presence of interactions when the chemical potential is tuned to a particular function of the other parameters. The ground states obtained are two-fold degenerate and differ in fermion parity, as is the case with the Kitaev/Majorana chain in a topological phase. We prove that the ground state is unique in each fermion parity sector and that there exists an energy gap. Furthermore, we investigate the effect of disorder in the chemical potential. We find that, like the non-interacting system, moderate disorder supports the topological phase, while at large disorder strengths the system becomes trivial.

We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures.
To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization
group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G(t) 1/sqrt(t), in sharp contrast
to the exponential decay in time predicted by conventional Luttinger liquid theory.

The concept of typicality states that a single pure state can have the same properties as the full statistical ensemble. This concept is not restricted to specific states and applies to the overwhelming majority of all possible states, drawn at random from a high-dimensional Hilbert space. In the cleanest realization, even a single eigenstate of the Hamiltonian may feature the properties of the full equilibrium density matrix, assumed in the well-known eigenstate thermalization hypothesis. The notion of property is manifold in this context and also refers to the expectation values of observables. Remarkably, typicality is not only a static concept and includes the dynamics of expectation values. Recently, it has become clear that typicality even provides the basis for powerful numerical approaches to the dynamics [1] and thermalization [2] of quantum many-particle systems at nonzero temperatures. These approaches are in the center of my talk.

In my talk, I demonstrate that typicality allows for significant progress in the study of real-time spin and energy dynamics of low-dimensional quantum magnets. To this end, I present a numerical analysis of current autocorrelation fuctions of the integrable XXZ spin-1/2 chain [1] and nonintegrable modifications with staggered magnetic fields [3] and inter-chain couplings [4]. This analysis includes a comprehensive comparison with state-of-the-art methods, including exact and Lanczos diagonalization, time-dependent density-matrix renormalization group, and perturbation theory. This comparison unveils that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both, integrable and nonintegrable systems. For the integrable case, I calculate the long-time dynamics of the spin current and extract the spin Drude weight for large systems outside the range of exact diagonalization. I particularly provide strong evidence that the high-temperature Drude weight vanishes at the isotropic point. For the nonintegrable cases, I obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of model parameters and temperature.

[1] R. Steinigeweg, J. Gemmer, and W. Brenig, Phys. Rev. Lett. 112, 120601 (2014).
[2] R. Steinigeweg et al., Phys. Rev. Lett. 112, 130403 (2014).
[3] R. Steinigeweg, J. Gemmer, and W. Brenig, Phys. Rev. B 91, 104404 (2015).
[4] R. Steinigeweg, J. Herbrych, X. Zotos, and W. Brenig, arXiv:1503.03871 (2015).

We develop a theory for the onset of inhomogeneous (FFLO) superconductivity in anisotropic electronic metals such as the charge transfer and Bechgaard salts in two dimensions. We show that that the resulting quantum-critical metal is distinctly different from previously considered cases and leads to pronounced non-Fermi liquid physics in hot regions of the Fermi surface. We compare our theory to recent thermodynamic and NMR measurements of κ(BEDT)2 Cu(NCS)2.

Recently, it has been demonstrated that the natural mineral linarite PbCuSO4(OH)2 can be described as a frustrated J1-J2 spin chain, with J1 as the ferromagnetic nearest neighbor interaction, and J2 the antiferromagnetic next nearest neighbor interaction. Here, a neutron diffraction and NMR study of the field-induced phases of linarite is presented for magnetic fields H parallel b axis at temperatures down to 1.5 K. A two-step spin-flop transition is observed, transforming the helical magnetic ground state into a collinear structure. Moreover, a magnetic phase with incommensurate sine-wave modulated moments parallel to the field direction was detected, enclosing the other long-range ordered phases, which in addition exhibits phase separation in high magnetic fields. As well, the incommensurability vector of the sine-wave modulated phase shifts with magnetic fields. Theoretical calculations suggest that this high field magnetic phase can be understood in terms of its field dependent multipolar character. 

In 5d Iridium oxides, a large spin-orbit coupling of ∼0.5 eV, inherent to heavy 5d elements, is not small as compared with other relevant electronic parameters, including Coulomb U, transfer t and crystal field splitting D, which gives rise to a variety of exotic magnetic ground states. In the layered perovskite Sr2IrO4, spin-orbital Mott state with Jeff=1/2 is realized due to the novel interplay of those energy scales [1-3]. Despite the strong entanglement of spin and orbital degrees of freedom, Jeff=1/2 iso-spins in Sr2IrO4 was found to be surprisingly isotropic, very likely due to a super-exchange coupling through almost 180° Ir-O-Ir bonds [4].  The temperature dependence of in-plane magnetic correlation length of Jeff=1/2 iso-spins, obtained from inelastic x-ray resonant magnetic scattering, was indeed well described by that expected for two-dimensional S=1/2 Heisenberg antiferromagnet [5].

The three-dimensional analog of Sr2IrO4, SrIrO3 perovskite is very close a band insulator due to lattice distortion but a Dirac semimetal protected by crystalline symmetry [6]. Upon increasing effective Coulomb U, magnetism emerges and creates a gap at Dirac nodes, giving rise to a semimetal to magnetic insulator transition. This can be realized by controlling the dimensionality and hence the effective U in (SrIrO3)m/SrTiO3 (m: number of SrIrO3 layer) super-lattice structure [7]. With reducing m, a transition to an insulator, accompanied with magnetism was clearly observed.   At m=1, single layer, the transport remains insulating even above the magnetic ordering temperature, indicative of the increased Mott character.

When Jeff=1/2 iso-spins interact with each other through 90° Ir-O-Ir bonds, very anisotropic bond dependent ferromagnetic coupling is expected, unique to strong SOC system. Complex Ir oxides with honeycomb and more recently identified hyper-honeycomb lattices [8], where x-, y- and z- 90° Ir-O-Ir bonds are realized, may be candidates for quantum spin liquid expected for the Kiatev model. Very likely due to the superposition of additional magnetic couplings not included in the Kitaev model [9], in reality, a long range magnetic ordering emerges at low temperatures in those compounds. Hyper-honeycomb β-Li2IrO3, though eventually show a marginal ordering, appears to be located at the critical vicinity to the Kitaev spin liquid.

1) B. J. Kim et al., Phys. Rev. Lett. 101, 076402 (2008).
2) B. J. Kim et al., Science 323, 1329 (2009).
3) S. Fujiyama et al., Phys. Rev. Lett. 112, 016405 (2014).
4) G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
5) S. Fujiyama et al., Phys. Rev. Lett. 108, 247212 (2012).
6) Chen, Y. et al. ,Nat. Commun. 6:6593 doi: 10.1038/ncomms7593 (2015).
7) J. Matsuno et al., Phys. Rev. Lett. (2015).
8) T.Takayama, et al., s Phys. Rev. Lett.114, 077202 (2015).
9) A.Kitaev, Annals of Physics 312 2 (2006).

In this talk I will give an overview of simulation methods for quantum systems in two and three spatial dimensions. I will, in particular, review the state of tensor network simulation methods including DMRG and PEPS, and of quantum Monte Carlo simulations for spins, bosons and fermionic systems.

Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R2/L2, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

[1] Phys. Rev. Lett. 114, 196401 (2015)

Majorana fermions were originally proposed as elementary particles acting as their own antiparticles. In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here we propose a physical system which realizes Landau levels - highly degenerate single-particle states usually resulting from an orbital magnetic field acting on charged particles - for Majorana fermions. This is achieved in a variant of a quantum spin system due to Kitaev which is distorted by triaxial strain. This strained Kitaev model displays a spin-liquid phase with charge-neutral Majorana-fermion excitations whose spectrum corresponds to that of Landau levels, here arising from a tailored pseudo-magnetic field. We show that measuring the dynamic spin susceptibility reveals the Landau-level structure by a remarkable mechanism of probe-induced bound-state formation.

We study the temperature-dependent quantum correction to conductivity due to the interplay of spin density fluctuations and weak disorder for a two-dimensional metal near an antiferromagnetic (AFM) quantum critical point. AFM spin density fluctuations carry large momenta around the ordering vector Q and, at lowest order of the spin-fermion coupling, only scatter electrons between "hot spots" of the Fermi surface which are connected by Q. Earlier it was seen that the quantum interference between AFM spin density fluctuations and soft diffusive modes of the disordered metal is suppressed, a consequence of the large-momentum scattering. The suppression of this interference results in a non-singular temperature dependence of the corresponding interaction correction to conductivity. However, at higher order of the spin-fermion coupling electrons on the entire Fermi surface can be scattered successively by two spin density fluctuations and, in total, suffer a small momentum transfer. This higher-order process can be described by composite modes which carry small momenta. We show that the interference between formally subleading composite modes and diffusive modes generates singular interaction corrections which ultimately dominate over the non-singular first-order correction at low temperatures. We derive an effective low-energy theory from the spin-fermion model which includes the above-mentioned higher-order process implicitly and show that for weak spin-fermion coupling the small-momentum transfer is mediated by a composite propagator. Employing the conventional diagrammatic approach to impurity scattering, we find the correction δ σ ∼ + log2 T for temperatures above an exponentially small crossover scale.