Current Trends in Strongly Correlated and Frustrated Systems

We study the effect of a small density $n_v$ of quenched non-magnetic impurities, {\em i.e.} vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable at small $n_v$ on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable at any nonzero $n_v$ due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) at nonzero $n_v$ due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally-packed dimer covers of the diluted lattice, and are fully supported by our computational results on $O(N)$ symmetric designer Hamiltonians.

We have studied the electron–electron interactions in the system composed of two metallic one-dimensional point contact and zero-sized wires, in the applied electric field and exposed to the influence of the external Zeeman magnetic field. The interactions between the electrons within wires have been taken into account within the usual Hubbard model. We have considered different limits of particle-filling on the atomic lattice site positions. We show the existence of the excitonic pairing in this one-dimensional system in different limits of the electron–electron interactions, magnetic field, and temperature. We demonstrate that the usual Hubbard-U interaction leads to strong electron localization, which enhances the local antiferromagnetic order in the system. We have shown that in the weak localization limit, with a small value of Hubbard-U potential, the magnetic field stabilizes the average charge fluctuations in the system and enhances the antiferromagnetic ordering in the bi-wire system. At the half-filling regime and at the zero value of the external magnetic field (when the maximum average occupation number on the lattice sites is 1), we got different behaviors of the excitonic order parameters for different spin orientations and the result does not change at different limits of the local Hubbard potential U. Furthermore, we found the temperature dependence of calculated physical quantities in the large-U limit and for the finite, large value of the Zeeman magnetic field. We claimed that the effect of Hubbard-U interaction on the excitonic order parameters is very similar to the effects of the magnetic field and temperature. Endeavor of the work, we have found that the principal effect of Hubbard-U interaction is to change the antiferromagnetic order parameter, and the large values of U increase considerably the antiferromagnetic order in the system, which is the manifestation of strong electron spin-localization on the atomic lattice site positions, thus proving the reminiscent artifact that the large-U limit is the strong Mott–Hubbard localization limit. We have found the excitonic phase transition in the system of coupled 1D metallic chains, which is the first proof to handle the complicated nature of electronic correlations in 1D electron systems. As the results showed in the paper, this is possible due to the simultaneous interplay of different physical parameters in the system, which could quench the strong charge density fluctuation nature of such 1D systems.

Kinetic magnetism is an iconic and rare example of collective quantum order that emerges from the interference of paths taken by a hole in a sea of strongly interacting fermions. Here the lattice topology plays a fundamental role, with odd loops frustrating ferromagnetism, as seen in recent experiments. However, the resulting magnetic order on a general graph has remained elusive. Here we systematically establish, using exact diagonalization, that local frustration centers on a grid strongly bind singlets while sharing a delocalized hole. This collective effect generalizes to random graphs, producing sharp and predictable variation with tunable frustration measures. Our findings demonstrate that one can shape the spin order as well as tune the net magnetization by embedding geometric frustration, opening up new avenues for spatially resolved quantum control of many-body systems. We outline a protocol to realize some of the key findings in existing cold-atom setups.

We investigate the effect of Hubbard and Kondo interactions on the edge states in the half-filled Su-Schrieffer-Heeger chain of electrons by studying the behavior of charge quasiparticles using Kumar representation and the density matrix renormalization group (DMRG) method. For any finite dimerization of hopping, by increasing the Hubbard interaction, the edge states are found to transmigrate from the physical charge gap to a high energy gap through an inter- mediate phase without the edge states. The extent of this phase with no edge states shrinks smoothly upon increasing the dimerization. The transmigration of edge states from the charge gap to the high energy gap is also found to occur with Kondo interaction, but through an intermediate phase which itself changes from having no edge states for weak dimerization to having the edge states in the physical as well as the high energy gaps coexisting from moderate to strong dimerization [1]. We also study the transmigration of edge states in other related one-dimensional models. [1] Jyoti Bisht, Somenath Jalal and Brijesh Kumar, Transmigration of edge states with interaction in Su-Schrieffer-Heeger Chain, Physical Review B 110, 245110 (2024)

For nearly three decades frustrated magnetism research in 3D has centered on the pyrochlore geometry of corner-sharing tetrahedra and the classical spin liquid (CSL) known as spin ice. In this talk I propose that a lattice of corner-sharing octahedra---appropriately dubbed the octochlore lattice---may provide the next-generation platform for 3D frustrated magnets, with realizations in anti-perovskite and certain potassium-flouride compounds. We study the phase diagram of Ising spins on the octochlore lattice with first- and second-neighbor interactions within each octahedron. In addition to a spin ice CSL, we identify a novel fracton CSL with excitations restricted to move on 1D lines, which is a classical U(1) analog of the celebrated X-cube model of fracton topological order. We characterize this fracton liquid from multiple perspectives---via its flat bands with nodal line touchings; as a condensate of spinon bound states; as a cage-net liquid; as a foliated fracton phase of intersecting spin vorticity models; and as a bionic spin liquid of intersecting square ice sheets---giving a comprehensive understanding of its excitations and connecting to many recent developments in the understanding of classical spin liquids. We also identify a fracton crystal phase, a crystalline arrangement of the fracton CSL excitations which exhibits quadrupolar nematic order. This works paves the way for the potential realization of fracton CSLs in real materials, while also demonstrating a constructive method for building classical fracton CSL models on a variety of lattices.

Using the combination of a new effective Hamiltonian approach and hybrid Monte-Carlo simulations, we unveil a variety of partially magnetically ordered (PMO) phases in the Kondo lattice model. Our approximation is motivated by two crucial features of the Hamiltonian: (i) formation of Kondo singlets leading to vanishing local magnetic moments, and (ii) spatially correlated nature of the effective single-particle kinetic energy. On a Square lattice, we discover PMO phases with fractional values $1/4$, $3/8$, and $1/2$ of Kondo-screened sites. A common understanding of these states emerges in terms of a non-local ordering mechanism. Our semiclassical approach can be generalized to study other interacting quantum systems in the intermediate coupling regime. By extending this effective Kondo lattice model to the Shastry-Sutherland lattice, we have captured field-induced fractional magnetization plateaus, reminiscent of those seen in rare-earth tetraborides.

We report disorder-free localization of Majorana fermions on intermediate time scales in an emergent gapless non-integrable quantum spin liquid. A large density of ground-state visons induced by an external magnetic field provides coherent flux disorder that (i) closes the Majorana fermion gap and (ii) localizes the fermions while preserving translation symmetry. The resulting Majorana metallic state is confirmed by the close agreement between the numerically obtained dynamical spin spectral function and the Majorana spectral function of an effective tight-binding model with coherent vison disorder. Compelling evidence of its localization is provided by the time evolution of the local energy density, which shows negligible spreading after a local quench on its ground state; and a vanishing energy current response despite the gapless energy spectrum. These results demonstrate that the disorder-free localization can also occur near equilibrium at low energy, and offer an explanation to the thermal paradox in recent experiments where a linear specific heat coexists with vanishing thermal transport in frustrated Mott insulators with neutral Fermi surfaces.

A very recent combined experimental and theoretical work by Shimizu et al.[1] on the star lattice antiferromagnet [(CH$_3$)$_2$]Cu$_3$(OH)(SO$_4$)$_4$·0.24 H$_2$O (Dimmethylammonium Copper Sulfate, DiMACuS for short), showed that no magnetic ordering takes place down to 0.1 K making this material a promising quantum spin liquid candidate. Their experimental findings, such as the peculiar magnetization response to an external magnetic field, were explained by the presence of sizeable anisotropic Dzyaloshinskii-Moriya interactions. In this work, we construct an effective low energy model for this system, which allows us to obtain the ground state configuration using a mean field approximation. We predict an ordered AFM state as the ground state configuration, addressing therefore the question of a quantum spin liquid state. The response of the system to an external magnetic field is reproduced, and we identify four different phases for non-zero magnetic field. Furthermore, the dynamical structure factor of the system is obtained by means of a multi-boson technique, revealing the gapless character of the ground state as well as explaining its elementary excitations. [1] Hajime Ishikawa, Yuto Ishii, Takeshi Yajima, Yasuhiro H. Matsuda, Koichi Kindo, Yusei Shimizu, Ioannis Rousochatzakis, Ulrich K. Rößler, Oleg Janson, Phys. Rev. B 109, L180401 (2024) [2] Marios Georgioum Oleg Janson and Ioannis Rousochatzakis, manuscript in preparation

Topological ordered phases have traditionally been considered to be beyond the Landau symmetry-breaking paradigm. Instead, these phases are characterized by their pattern of long-range quantum entanglement. Recently, however, topological order has been reinterpreted in an extended Landau paradigm as emerging from the spontaneous breaking of higher-form symmetry. In the toric code, for example, these higher-form symmetry operators are the non-contractible Wilson loops on the torus. We connect this symmetry-breaking to quantum information via the entanglement asymmetry, which measures of how much entanglement is encoded in the broken symmetry. Besides extending entanglement asymmetry to the broader class of higher-form symmetries, we find that for topologically ordered phases, this asymmetry matches the topological entanglement entropy (TEE). Entanglement asymmetry therefore offers a new path to calculate the TEE, which typically is extracted from a complicated subtraction scheme involving multiple entanglement entropies. We also uncover the role of entanglement asymmetry in other theories with higher-form symmetries, like Maxwell electrodynamics, and for non-invertible symmetries. In all of these cases, the entanglement asymmetry captures a subleading topological contribution to the entanglement entropy.

We have developed a new, exact mathematical technique that we call statistical physics perturbation theory [1]. Our method supersedes the high-temperature series expansion and is also competitive with Monte Carlo simulations. Indeed, we do not require the assumption of a phase transition to predict one! Our perturbation theory is for operators related by the Baker-Campbell-Hausdorff (BCH) identity, $\exp(C)=\exp(A)\exp(B)$ [2], rather than by addition, $C=A+B$, as in quantum mechanics. We use the transfer matrix approach to classical statistical mechanics [3] which leads directly to the BCH identity and we must find the operator $C$. Our perturbation theory is almost verbatim the quantum case, save that the denominators, $1/x$, are replaced by hyperbolic functions, $\coth(x)$, and corrections! We also present predictions for the correlation length as a function of temperature and the associated critical exponent for the Ising model on the square, cubic and hypercubic lattices. Surprisingly, for the square lattice, we find the exact correlation length at first order with all higher order contributions vanishing! [1] J. M. Jones and M. W. Long, in preparation [2] J. C. Moodie and M. W. Long, 2021 J. Phys. A: Math. Theor. 54 015208 [3] T. D. Schultz, D. C. Mattis and E. H. Lieb, Rev. Mod. Phys. 36, 85

Abstract Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a finite chain are calculated. The winding number invariant reflects the topological nature of the electron liquid. The phase diagram includes two topological phases with different winding number invariants, the topologically trivial Mott insulator phase, and three critical phase transition points. Numerical calculations confirm and illustrate the analytical results. Conclusion An exactly solvable 1D model of interacting electrons is proposed, which takes into account the on-site Hubbard interaction and correlated hoppings between electrons located at the next-nearest neighbor sites. The ground state phase diagram of the model is rich, it includes two topological phases with different winding number invariants and a trivial topological phase of the Mott insulator (MI). In the topological phases, zero-energy Majorana edge modes and winding number invariant determine the topological state of the electron liquid. Taking into account open boundary conditions, eigenvalues and eigenvectors of the model Hamiltonian have been obtained and illustrated by numerical calculations. Our exact analytical results for a finite modified Kitaev-Hubbard chain provide a new insight into the behavior of the electron liquid in the topological and Mott insulator phases. We have delved into their nature and elucidated that there is a critical value of the amplitude repulsion interaction between fermions, which leads to the transition from the topological to MI phase of the electron liquid. The results are obtained within the framework of 1D exactly solvable models and contribute to the understanding of the topological to MI transition.

Altermagnets present a new class of fully compensated collinear magnetic order, where the two sublattices are not related merely by time-reversal combined with lattice translation or inversion, but require an additional lattice rotation. This distinctive symmetry leads to a characteristic splitting of the magnon bands; however the splitting is only partial -- residual degeneracies persist along certain lines in the Brillouin zone as a consequence of the underlying altermagnetic rotation. We consider a two-dimensional $d$-wave altermagnetic spin model on the checkerboard lattice and introduce additional interactions such as an external magnetic field and Dzyaloshinskii-Moriya interactions, that lift these degeneracies. The resulting magnon bands become fully gapped and acquire non-trivial topology, characterized by nonzero Chern numbers. We demonstrate the crucial role of altermagnetism for the generation of the Berry curvature. As a direct consequence of the topological magnons, we find finite thermal Hall conductivity $\kappa_{xy}$, which exhibits a characteristic low-temperature scaling, $\kappa_{xy}\propto T^4$. Moreover, $\kappa_{xy}$ changes sign under reversal of the magnetic field, exhibiting a sharp jump across zero field at low temperatures. We also demonstrate topologically protected chiral edge modes in a finite strip geometry.

Weak first-order pseudocriticality with approximate scale invariance has been observed in a variety of settings, including the intriguing case of deconfined criticality in 2+1 dimensions. Recently, this has been interpreted as extremely slow flows ("walking behavior") for real-valued couplings in proximity to a bona fide critical point with complex-valued couplings, described by a complex conformal field theory (CFT). Here we study an SU($N$) generalization of the the Heisenberg antiferromagnet, which is a familiar model for deconfined criticality in 2+1 dimensions. We show that in 1+1 dimensions the model is located near a complex CFT, whose proximity can be tuned as a function of $N$. We employ state-of-the-art quantum Monte Carlo simulations for continuous $N$ along with an improved loop estimator for the Renyi entanglement entropy based on a nonequilibrium work protocol. These techniques allow us to track the central charge of this model in detail as a function of $N$, where we observe excellent agreement with CFT predictions. Notably, this includes the region $N>2$, where the CFT moves into the complex plane and pseudocritical drifts enable us to recover the real part of the complex central charge with remarkable accuracy. Since the present model with $N=3$ is also equivalent to the spin-1 biquadratic model, our work sheds new light on the dimerized phase of the spin-1 chain, demonstrating that it is pseudocritical and proximate to a complex CFT.

The Shastry-Sutherland model, a hallmark of frustrated magnetism, is realized in SrCu$_2$(BO$_3$)$_2$, where competing intra- and inter-dimer interactions $J$ and $J'$ stabilize a dimerized ground state. A generalized anisotropic version of this model, with inequivalent couplings $J_1$ , $J_2$ and $J'_1$ , $J'_2$, has been predicted to host novel ground states [1] and may help to resolve the debate [2] on the nature of the plaquette phase of SrCu$_2$(BO$_3$)$_2$. Experimentally, anisotropic strains break the tetragonal symmetry of SrCu$_2$(BO$_3$)$_2$ and can be used to tune the anisotropy in the Shastry-Sutherland model. We employ the AC elastocaloric effect, a thermodynamic probe of strain-tuned quantum materials [3], to map the entropic landscape of SrCu$_2$(BO$_3$)$_2$ under large anisotropic strains. By comparing the results under [100] and [110] strains, we disentangle symmetry-breaking from symmetry-preserving effects, revealing features consistent with hydrostatic-pressure studies [4], along with new effects likely arising from symmetry breaking. Complementary x-ray diffraction under uniaxial pressure and DFT calculations elucidate the evolution of the lattice structure with strain and its effect on magnetic properties. We explore the potential of using the experimental data to model the elastocaloric phase diagram through METTS simulations [5], with exchange parameters derived from DFT calculations. [1] Boos et al, PRB 100, 140413(R) (2019) [2] Zayed et al, Nat. Phys. 13, 962 (2017) [3] Ikeda et al, RSI 90, 083902 (2019) [4] Guo et al, PRL 124, 206602 (2020) [5] Wang et al, arXiv:2405.18484 (2024) Authors: Francisco Lieberich$^{1,6}$, Rafael Soares$^2$, Pascal Puphal$^3$, Ekaterina Pomjakushina$^4$, Tobias Ritschel$^6$, Oleg Janson$^5$, Alexander Wietek$^2$, Jochen Geck$^6$, Elena Gati$^{1,6}$ $^1$ Max Planck Institute for Chemical Physics of Solids, Dresden, Germany $^2$ Max Planck Institute for the Physics of Complex Systems, Dresden, Germany $^3$ Max Planck Institute for Solid State Research, Stuttgart, Germany $^4$ Paul Scherrer Institute, Villigen, Switzerland $^5$ Leibniz Institute for Solid State and Materials Research, Dresden $^6$ Technical University of Dresden, Dresden, Germany

We study classical dipole-octupole pyrochlore spin systems in an external magnetic field along the \([111]\) direction. We identify a low temperature symmetry-breaking phase as a fragmented spin liquid. This phase is characterized by the coexistence of three phenomena: a \(U(1)\) spin liquid in the Kagome planes, spontaneous \(Z_2\) symmetry breaking, and partial spin polarization. We show that even without dipolar interactions, the dipole components form a spin liquid stabilized by the octupolar degrees of freedom. This physics manifests experimentally as shadow pinch points: low-intensity pinch-point features underlying strong Bragg peaks. We discuss how these discoveries apply to experimentally discovered materials.

While moiré phenomena have been extensively studied in low-carrier-density systems such as graphene and semiconductors, their implications for metallic systems with large Fermi surfaces remain largely unexplored. Using GPU-accelerated large-scale ab-initio quantum transport simulations, we investigate spin transport in two distinct platforms: twisted bilayer MoTe2 (semiconductor, from lightly to heavily doping) and NbX2 (X = S, Se; metals). In twisted MoTe2, the spin Hall conductivity (SHC) evolves from 4e/4π at 5.09∘ to 10e/4π at 1.89∘, driven by the emergence of multiple isolated Chern bands. Remarkably, in heavily doped metallic regimes--without isolated Chern bands--we observe a universal amplification of the spin Hall effect from Fermi surface reconstruction under long-wavelength potential, with the peak SHC tripling from 6e/4π at 5.09∘ to 17e/4π at 3.89∘. For prototypical moiré metals like twisted NbX2, we identify a record SHC of −17e/4π (-5200 (ℏ/e)S/cm in 3D units), surpassing all known bulk materials. These results establish moiré engineering as a powerful strategy for enhancing spin-dependent transport, and advancing ab-initio methodologies to bridge atomic-scale precision with device-scale predictions in transport simulations.

Spatial modulation of magnetic moments is quite ubiquitous in electronic systems, known as spin-density waves, while not much is known in insulating magnets, as in most cases like spiral or chiral states, the spins gradually change its orientations keeping its amplitude constant. Here, we find an emergent dipole–quadrupole hybridized magnetic phase in spin–orbit-coupled pseudospin-1 pyrochlore magnets with Fe2+ ions [1]. This work is motivated by the experimental observation of amplitude modulation of magnetic moments in the insulating spinel magnet GeFe2O4 [2]. Starting from a microscopic model, we derive the low-energy effective spin Hamiltonian, in which the spin–orbit-coupled nature of the pseudospin-1 state and the crystal field effect give rise to anisotropic exchange interactions ($J_{zz}$, $J_{\pm}$, $J_{\pm\pm}$, $J_{z\pm}$) and a single-ion anisotropy term D. We apply an SU(3) mean-field theory that treats dipole and quadrupole moments on equal footing. This contrasts with the previous spin-1 theories, which typically yield either purely dipolar or quadrupolar ordered phases in the SU(2) framework. In the resulting magnetic phase diagram, we find a spontaneous fragmentation of spin-1 into the exotic sublattice configurations having a nonuniform spatial distribution of dipole and quadrupole moments. We ascribe this phase to the interplay of $J_{z\pm}$ and D, and discuss the relevance with the experimental observations in GeFe2O4 [2]. [1] H. Nakai and C. Hotta, arXiv:2411.15969 [2] G. Perversi et al., Commun. Phys. 1, 69 (2018).

We present the Stagome lattice, a variant of the Kagome lattice, where one can make any of the bands completely flat by tuning an externally controllable magnetic flux. This systematically allows the energy of the flat band to coincide with the Fermi level. We have analytically calculated the compact localized states associated to each of these flat bands appearing at different values of the magnetic flux. We also show that, this model features nontrivial topological properties with distinct integer values of the Chern numbers as a function of the magnetic flux. We argue that this mechanism for making any of the bands exactly flat could be of interest to address the flat-band superconductivity in such a system. Additionally, we show that our results are robust even in the presence of a small amount of disorder. Furthermore, we believe that the phenomenon of photonic flat band localization could be studied in the Stagome lattice structure, designed for instance using femtosecond laser-induced single-mode waveguide arrays.

In BCS-superconductors, the spectral gap, $E_\text{g}$, the pairing amplitude, $\Delta$, and the mean-field critical temperature $T_\text{c0}$ are essentially identical energy scales. This is no longer the case in the presence of sufficiently strong disorder, where the superconductor-insulator transition (SIT) is approached. Moreover, in BCS-theory the superfluid density stiffness, $J_\text{s}$, is fully determined by $\Delta$ and the normal state resistance $T_\text{N}$, but this relation no longer holds in the presence of strong disorder, so that $J_\text{s}$ becomes a scale of its own right. Recent experiments have determined $J_\text{s}(T)$ in ultra-thin NbN films by measuring kinetic inductance and found a sharp Berezinski-Kosterlitz-Thouless (BKT) transition. We present numerical calculations of the superfluid stiffness, obtained from the Boguliubov-de~Gennes (BdG) theory of disordered samples in a very broad range of disorder strengths. We do calculations at unprecedented system sizes large enough to capture the effect of mesoscopic wavefunction fluctuations on $J_\text{s}(0)$. We also present complementary experimental data for $J_\text{s}(T)$ over a wide range of disorder strength. A detailed comparison of our computational results with the measurements will be presented.

The experimental signature of topological charge density wave(TCDW) has been reported on twisted mono - bilayer graphene(TMBG) at filling factor $\nu = 3/2$ and $\nu = 7/2$. Theoretically, this can be described by partially filling the Chern 2 band emerging from TMBG, which allows Coulomb interaction to spontaneously break the moire translation symmetry and split into two Chern 1 bands. However, it is still not clear how the correlated ground states of TMBG between integer and half integer filling are connected. In this work, we study the competition between CDW and non-CDW states of the TMBG for positive half integer filling by performing unbiased Hartree - Fock calculation. We argue that TCDW can be energetically favorable for entire positive half integer filling, which affects the strength of other orders such as flavor polarized order, intervalley coherent order, etc. In addition, we study how the proximitized spin orbit coupling(SOC) effect induced by putting transition metal dichalcogenide material on top of TMBG can affect the competition between CDW and non - CDW orders. We found that even though small SOC parameters described by Ising and Rashba terms still allows CDW to be more energetically favored than non -CDW state, SOC can change the strength of orders dramatically, especially for the spin - mixing related order. Finally, by allowing the translation symmetry breaking momentum vector to be the entire three M points in moire Brillouin zone, we discuss how the SOC affects the energetic competition between tetrahedral antiferromagnet and TCDW.

We investigate the evolution of crystal structure, magnetic, thermodynamic, and spin correlation behaviors in a series of double perovskite materials Sr$_2$NiMo$_{1-x}$W$_x$O$_6$ (0 $\le x \le$ 1) using magnetic susceptibility (dc and ac), specific heat, and neutron diffraction measurements. The magnetic Ni$^{2+}$ (3$d^8$, spin-1) and Mo$^{6+}$/W$^{6+}$ (4$d^0$/5$d^0$) ions are alternately arranged in the crystal lattice, where the (super)exchange interactions between Ni$^{2+}$ follow the Ni–O–Mo/W–O–Ni pathways. Our magnetization measurements reveal an antiferromagnetic ground state in the parent compound ($x$ = 0.0) with an ordering temperature $T_N$ $\sim$ 80 K, which is progressively suppressed upon W substitution, reaching $T_N$ $\sim$ 60 K for the end member ($x$ = 1.0). Furthermore, W substitution induces an additional low-temperature feature, evident from the bifurcation between zero-field-cooled and field-cooled moments, indicating the presence of a coexisting glassy phase, as identified via ac susceptibility in the representative $x$ = 0.5 sample. Specific heat data exhibit a clear anomaly across $T_N$, and the magnetic component follows a $C_m$ $\propto$ $T^3$ dependence at low temperature, consistent with antiferromagnetic spin-wave excitations. Neutron diffraction measurements confirm a long-range antiferromagnetic ground state with a magnetic propagation vector $k$ = (0.5, 0, 0.5), and the ordered magnetic moment is found to be close to the expected value of $\sim$ 2 $\mu_B$/Ni$^{2+}$ across the series. While W substitution does not significantly modify the lattice or magnetic structure, it reduces $T_N$ and introduces a sizable magneto-structural coupling near the ordering temperature. Although Mo and W share similar ionic radii, charge states, and nonmagnetic nature, the difference in their $d$-orbital character (4$d^0$ vs. 5$d^0$) plays a crucial role in influencing the magnetic ground state. These results highlight the importance of further investigations using microscopic probes and theoretical calculations.

Local integrals of motion (LIOMs) play a key role in understanding the long-time properties of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their structure can also be studied via numerical methods, which, however, involve exact diagonalization of Hamiltonians, posing a bottleneck for such studies. We show that finding LIOMs in translationally invariant lattice models or unitary quantum circuits can be reduced to a problem for which one may numerically find an exact solution in the thermodynamic limit. We develop a simple algorithm and demonstrate the efficiency of this method by calculating LIOMs and bounds on correlations (the Mazur bounds) for infinite integrable spin chains and unitary circuits. Finally, we demonstrate that this approach identifies slow modes in nearly integrable spin models and estimates their relaxation times.

The prominent Anderson localization phenomenon is known to be crucially dependent on the disorder being present in the system. In the present study we demonstrate that localization could arise in a completely disorder free system, namely in a quasi-1D infinite $U$ Hubbard model at half filling doped by a single hole in all spin sectors for low temperatures. By analytical considerations we show that this observation is a direct consequence of an effective kinetic energy frustration within this model and explicitly analyze the localization length behavior as a function of relative hopping amplitudes. Furthermore, we rigorously prove that within each spin sector the ground state of the model is the dimerized state comprised of singlet and triplet spin pairs, with unbroken chain of singlets forming the bulk of the hole's localized wavefunction. Our results could be used for the broader context of RVB states in Hubbard models.

We introduce a bond-dependent spin-$\frac{1}{2}$ model characterized by locally conserved, anticommuting $\mathbb{Z}_2$ charges, which lead to an extensively degenerate ground state and spin-liquid behavior. The model’s ground-state degeneracy results in a finite residual entropy, resulting from its distinctive site-sharing lattice geometry. Using exact diagonalization that exploits local $\mathbb{Z}_2$ symmetries, we analyze the energy-level statistics and identify features suggestive of eigenstate thermalization breakdown and Hilbert space fragmentation.

Magnetic monopoles have long been sought after in fundamental physics. In recent years, spin ice materials have emerged as a canonical platform where emergent magnetic monopole-like excitations arise naturally from the underlying spin configurations [1]. These systems belong to the broader class of frustrated magnets, which, unlike conventional ferromagnets and antiferromagnets, show strong correlations without long-range order even at very low temperatures. The spin ice model has been instrumental in understanding such exotic phases, particularly the Coulomb spin liquid phase [2], where fractionalized excitations manifest as magnetic monopoles. The dynamics of these emergent monopoles have been studied before [3], but much less is known about their behaviour in inhomogeneous environments. In our work, we have looked at their dynamics in the presence of a domain wall within the Fragmented Coulomb Spin Liquid (FCSL) phase. Particularly, we have focused on how the nature of magnetic monopoles changes and their departure from the pure Coulomb phase under different domain wall configurations. 1. C. Castelnovo, R. Moessner, and S. Sondhi. Magnetic monopoles in spin ice. Nature, 451:42–45,2008. 2. Christopher L. Henley. The “Coulomb phase” in frustrated systems. Annual Review of Condensed Matter Physics, 1(1):179–210, 2010. 3. L. D. C. Jaubert, ”Monopole Holes in a Partially Ordered Spin Liquid,” SPIN 5, 1540005 (2015).

Frustrated magnets are a playground for exotic physics. They host quantum states that are disordered, entangled, topological or fractionalized. A broad class of such disordered states fall under the umbrella of quantum spin liquids (QSLs). Resonating Valence Bond (RVB) theory posits QSL wavefunctions described as linear superpositions of singlet coverings[2]. A general method for studying such RVB QSLs is to treat the excitations as ‘fractionalized’ particles [2, 3]. The spin operators are rewritten in terms of these new entities, leading to emergent gauge theories [3, 4]. This typically involves a mean-field approximation, with a projection onto the physical Hilbert space [2]. This projection introduces non-trivial correlations in an otherwise ordinary Hartree-Fock ground state. The parton construction has been validated by many successes including the Kitaev Honeycomb model [4]. However, it cannot be easily interpreted in terms of the physical spins that constitute the magnet. A recipe to construct an explicit wavefunctions in the spin-basis can bridge this gap. Moreover, it can demonstrate the character of valence bonds and resonance as promised by the RVB picture. We provide a recipe for spin-basis wavefunctions for 1D and quasi-1D Kitaev-like models (and generalized compass models). Our work builds upon the results of [5]. The spin-1/2 models are Jordan-Wigner integrable, while higher spin versions are not. Our wavefunctions are inspired by a perturbative approach starting from the an anisotropic limit. They are validated by comparison with exact-diagonalization and a variational approach. We point to intriguing topological character that encodes long-ranged correlations. Our approach generalizes the RVB picture to Hamiltonians that explicitly break spin-rotation symmetry. It can lead the way to spin-wavefunction-based approaches for 2D QSLs with topological order [4]. [1] Alwyn Jose Raja, Rajesh Narayanan, R. Ganesh (manuscript in preparation) [2] Baskaran, G., Z. Zou, and P. W. Anderson. ”The resonating valence bond state and high-T c superconductivity-a mean field theory.” Solid State Communications 63, no. 11 (1987): 973-976. [3] Affleck, Ian, Z. Zou, T. Hsu, and P. W. Anderson.“SU (2) gauge symmetry of the large-U limit of the Hubbard model.” Physical Review B 38, no. 1 (1988): 745. [4] Kitaev, Alexei. “Anyons in an exactly solved model and beyond.” Annals of Physics 321, no. 1 (2006): 2-111. [5] Gordon, Jacob S., and Hae-Young Kee.“Insights into the anisotropic spin-S Kitaev chain.” Physical Review Research 4, no. 1 (2022): 013205.

Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet ground state. In this work, we introduce a three-dimensional analogue of the SS lattice, constructed by deforming the pyrochlore lattice to preserve the local SS geometry while extending the connectivity in three dimensions. Despite the dimensional increase and altered topology, the ground-state phase diagrams of classical Ising and Heisenberg spins remain analytically tractable and closely follow their 2D counterparts, including the existence of a $1/3$ magnetization plateau and umbrella states. Most notably, for quantum spins $S=1/2$, the dimer singlet state survives as an exact ground state over a finite region of the phase diagram. We argue, using exact diagonalization, that the singlet phase is stabilized beyond its 2D counterpart, suggesting enhanced robustness in three dimensions. These results offer a rare, controlled platform to explore the impact of dimensionality on quantum frustration, exact solvability, and potential spin liquid behavior in 3D, with relevance to emergent topological and magnetic phases.

Abstract: In frustrated magnetism, the empirically discovered quantum-to-classical correspondence (QCC) matches the real-space static susceptibility pattern of a quantum spin-1/2 model with that of its classical counterpart computed at an elevated effective temperature. This striking correspondence, first observed via bold-line diagrammatic Monte Carlo simulations in two and three dimensions, holds within error bars down to temperatures an order of magnitude below the exchange coupling J. In this talk, we explore the analytical foundation and inherent limitations of QCC using dynamic high-temperature series expansions (Dyn-HTE), carried out to twelfth order in J/T. We show that the static susceptibility of a variety of quantum Heisenberg models in d>1 dimensions is remarkably well approximated by a renormalized mean-field (MF) ansatz. This effective form arises from partial cancellations among high-order diagrams and retains its accuracy deep into the cooperative paramagnetic regime, thus providing an explanation for the surprising universality of QCC observed across a variety of frustrated lattices. We illustrate this framework across all models previously discussed in the context of QCC, including the recently experimentally studied S=1 material $\mathrm{K}_2\mathrm{Ni}_2(\mathrm{SO}_4)_3$.

We present 2D $\cot{\Theta_H}$ and resistivity calculations in the Extremely Correlated Fermi Liquid theory framework.

The sawtooth chain, otherwise known as the $\Delta$ chain, has a long history as a minimal model of frustrated magnetism, serving as a realization of Shastry-Sutherland type solitons. Pertaining to material realizations, like delafossite, euchroit, atacamite, etc, there will generically be residual couplings between chains. Motivated by this we study the nearly ideal sawtooth chains, weakly coupled to neighboring chains. We analyze the classical model, revealing 2D emergent system size scaling degeneracies in the 3D coupled model. Leading order quantum fluctuations are also discussed.

Using a recently developed variational method, the so-called Ghost Gutzwiller wave function, we show how a paramagnetic spin liquid insulator can be stabilized in the half-filled single-band Hubbard model. This phase hosts quasiparticles that are crucial to yield the paramagnetic response without showing up in the single-particle spectrum, and, as such, they can be legitimately regarded as an example of Anderson’s spinons. In our work, we investigate the interface between a system in the spin liquid phase and a metal. We demonstrate how spinons at the interface regain charge through the proximity effect, reemerging in the spectrum as a heavy-fermion band. Additionally, the system exhibits critical behavior near the metal-Mott insulator transition, as evidenced by the evolution of the quasiparticle residue and the density across the interface. Finally, we argue that when the bulk transition is first-order, the critical behavior observed at the interface belongs to the universality class of wetting transitions.

Heterostructures that combine topological insulators and superconductors provide an exciting platform to explore exotic quantum states, such as topological superconductivity and Majorana bound states. In this work, we design and study a heterostructure made of Bi$_{2-x}$Sb$_{x}$Te$_{2}$S (BSTS), a topological insulator with a well-insulating bulk, placed in contact with the layered superconductor NbSe$_{2}$. Using advanced electron beam lithography and a careful stacking technique, we fabricated devices with controlled BSTS thickness and clean interfaces. This setup allows us to probe how superconductivity from NbSe$_{2}$ is transferred into the surface states of BSTS through the proximity effect. Spectroscopic measurements confirm that superconducting correlations are induced in the topological surface states. Under an applied magnetic field, we observe features consistent with localized zero-energy modes in vortex cores, which may be signatures of Majorana bound states, as predicted in similar topological insulator/superconductor systems. Our results demonstrate that BSTS/NbSe$_{2}$ heterostructures are a promising platform for realizing topological superconductivity and open the door to further studies of quantum phenomena relevant to topological quantum computing.

The study of competing orders in two-dimensional quantum magnets was strongly motivated by the prediction of non-Landau quantum phase transitions, but often we found symmetry-enhanced first-order transitions or pseudo-criticality with a logarithmic drift of critical exponents. Here we present results for a (0+1) dimensional spin-boson model where all of these phenomena occur due to a fixed-point annihilation within the critical manifold. Our recently-developed wormhole quantum Monte Carlo method for retarded interactions allows us to study the critical properties of this model with unprecedented precision. We find a tunable transition between two ordered phases that can be continuous or first-order, and even becomes weakly first-order in an extended regime close to the fixed-point collision. We provide direct numerical evidence for pseudo-critical scaling on both sides of the collision manifesting in an extremely slow drift of critical exponents. We also find scaling behavior at the symmetry-enhanced first-order transition as described by a discontinuity fixed point. Our study motivates future work in higher-dimensional quantum dissipative spin systems.

The transition metal dichalcogenide (TMD) moiré system has recently emerged as a platform for realizing Hubbard physics, promising to capture the interplay among strong electron correlations, magnetism, and band topology. In a honeycomb lattice with a vertical electrostatic gating field that breaks the particle-hole symmetry, we identify a mechanism for ferromagnetism at integer filling factors without the need for Hund's coupling. Using ED, DMRG calculations, and perturbation theory, we show that ferromagnetism occurs in a critical charge-transfer regime and remains stable in the presence of complex hopping amplitudes and slight doping. Our theory helps explain the experimentally observed ferromagnetism that stabilizes a zero-field Chern insulator in R-stacked twisted bilayer $tMoTe_2$ near filling factor $\nu_h=1$ at intermediate gate fields.