We study many-body localization (MBL) in a nearest-neighbor hopping 1D lattice with a slowly varying (SV) on-site potential $U_j=\lambda cos\left(\pi \alpha j^s\right)$ with $0<s<1$. The corresponding noninteracting 1D lattice model is known to have single-particle localization with mobility edges. Using exact diagonalization, we find that the MBL of this model has similar features to the conventional MBL of extensively studied random or quasiperiodic (QP) models, including the transitions of eigenstate entanglement entropy (EE) and level statistics, and the logarithmic growth of EE. To further investigate the universal properties of this MBL transition in the asymptotic regime, we implement a real-space renormalization group (RG) method. RG analysis shows a subvolume scaling $\sim L^{d_{\mathrm{MBL}}}$ with $d_{\mathrm{MBL}}\approx 1-s$ of the localization length (length of the largest thermal clusters) in this MBL phase. In addition, we explore the critical properties and find universal scalings of the EE and localization length. From these quantities, we compute the critical exponent $\nu$ using different parameters $s$ (characterizing different degrees of spatial variation of the imposed potential), finding the critical exponent staying around $\nu \approx 2$. This exponent $\nu \approx 2$ is close to that of the QP model within the error bars but differs from the random model. This observation suggests that the SV and QP models may belong to the same universality class, which is, however, likely distinct from the random universality class.

We theoretically investigate the intrinsic anomalous Hall effect in two magnetically ordered systems: One is the ferromagnetic dipole system, and the other is the anisotropic magnetic dipole system, the latter of which has been proposed as a microscopic indicator of the anomalous Hall effect in antiferromagnets with the negligibly small magnetization. We show their similarity and difference in the anomalous Hall effect by analyzing the fundamental tight-binding model on a two-dimensional square lattice. We find that the magnitudes of the anomalous Hall effect in the two systems are similar to each other, while the magnetization in the anisotropic magnetic dipole system is much smaller than that in the ferromagnetic dipole system; this indicates that the microscopic mechanisms are different from each other. We show that such a difference appears in the momentum-resolved Berry curvature resulting from the different types of magnetic order parameters, giving rise to distinct gap-opening behaviors. We also show that the anomalous Hall effect in the anisotropic magnetic dipole system is enhanced when the magnitude of the spin-orbit coupling is smaller than that of the magnetic mean field. Our results provide a possibility of the giant anomalous Hall effect in collinear and coplanar antiferromagnetic systems with the anisotropic magnetic dipole.

In this work, we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free-fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a universality class with unusual critical exponents. We also emphasize the ability of the Loschmidt echo to characterize potential topological phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.

$\alpha \text{−}{\mathrm{RuCl}}_3$ has attracted significant attention as a prime candidate for the spin-1/2 Kitaev spin liquid in two-dimensional honeycomb lattices. Although its ground state is magnetically ordered, the order is suppressed under a moderate in-plane magnetic field. The intermediate regime of the field has exotic behaviors, some of which are claimed to originate from a Kitaev spin liquid. In resolving debates surrounding these behaviors, interlayer interactions in $\alpha \text{−}{\mathrm{RuCl}}_3$ have been largely overlooked due to their perceived weakness in van der Waals materials. However, near the transition they may become significant as the field energy approaches the interlayer coupling scale. Here we investigate the effects of interlayer couplings in $\alpha \text{−}{\mathrm{RuCl}}_3$ with $R\overline{3}$ and $C2/m$ structures. We first examine their effects on the transition temperature $\left(T_N\right)$ using classical Monte Carlo simulations. We found that the interlayer couplings have minimal effects on $T_N$, and the different $T_N$ between the two structures are mainly due to the anisotropy in intralayer interactions. Focusing on the $R\overline{3}$ structure, we show that the nearest-neighbor interlayer interaction is the XXZ type due to the symmetry, and the next-nearest-neighbor interaction of the Kitaev type is crucial for the transition between two zigzag orders under an in-plane field. Furthermore, an intermediate phase with a large unit cell emerges due to the interlayer interactions. Our findings provide insights into the exotic behaviors and sample dependence reported in $\alpha \text{−}{\mathrm{RuCl}}_3$.

Magnonic black holes—analogue event horizons for the spin-wave collective excitations of ordered magnets—can be used for fundamental research, for example, for investigating Hawking radiation, but also for technological applications of spin waves. Here we show how to engineer a horizon for spin waves in antiferromagnets, which have the attractive feature of fast magnetization dynamics and linear dispersion relation. We propose a setup with spatially varying exchange interaction with spin-transfer torque to implement the horizon and a second setup for the amplification of spin waves consisting of an antiferromagnet subject to a spatially varying external magnetic field that is driven by spin orbit torque. We compute the values of parameters needed to implement the horizon and to have amplification of spin waves. We develop the corresponding Klein-Gordon equation and quantify the amplification. Our paper paves the way for investigation of Hawking radiation of spin waves and for antiferromagnet-based spin-wave amplifiers.

Recently, evidence of superconductivity (SC) with onset $T_c$ above the McMillan limit has been detected in the ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ ultrathin film grown on the ${\mathrm{LaSrAlO}}_4$ substrate at ambient pressure. This progress opens another era in the field of the nickelate superconductors. Here we perform a density-functional-theory (DFT) based calculation for the band structure of this material. The obtained $\mathrm{DFT}+U$ band structure has the feature that the bonding $d_{z^2}$ band crosses the Fermi level, forming the hole pocket $\gamma$, consistent with the angle-resolved photoemission spectrum (ARPES). Taking the low-energy Ni-$(3d_{z^2},3d_{x^2-y^2})$ orbitals placed on the tetragonal lattice structure, we construct a 2D bilayer four-band tight-binding model which well captures the main features of the $\mathrm{DFT}+U$ band structure. Then considering the multiorbital Hubbard interaction, we adopt the random-phase approximation (RPA) approach to investigate the pairing nature. The obtained pairing symmetry is $s^{\pm }$ or $d_{xy}$ for the hole-doping level $\delta$ below or above 0.12, induced by the different Fermi surface nesting situations. For the realistic $\delta =0.21$ measured by the ARPES, our RPA calculations obtain the next-nearest-neighbor pairing $d_{xy}$-wave SC dominated by the $d_{z^2}$ orbital, consistent with the experimental observation that the $T_c$ enhances with the shrinking of the in-plane lattice constants. This pairing state is induced by the nesting between the different patches within the $\gamma$ pocket. Our results are appeal for experimental verifications.

$\alpha \text{−}{\mathrm{Li}}_x{\mathrm{V}}_2{\mathrm{O}}_5$ is obtained by intercalating Li between the layers of ${\mathrm{V}}_2{\mathrm{O}}_5$. The partial filling of the split-off conduction band by electron donation from Li leads to significant changes in optical properties. Here we study the electronic band structure of $\alpha \text{−}{\mathrm{LiV}}_2{\mathrm{O}}_5$ using quasiparticle self-consistent (QS) $GW$ calculations and the optical dielectric function by means of the Bethe-Salpeter equation (BSE). The half filling of the narrow split-off band leads to a spin splitting and formation of magnetic moments of $0.5{\mu }_B$ per V which order antiferromagnetically along the chain or $b$ direction. The imaginary part of the dielectric function shows a very strong optical absorption band near 2 eV for polarization along the $a$ direction already in the independent particle approximation but redshifted in the BSE. It is about ten times stronger in intensity than the lowest exciton peaks in pure ${\mathrm{V}}_2{\mathrm{O}}_5$ or than the $b$ direction. This absorption stems from a localized transition between the occupied V-$d_{xy}$ derived band, which is odd with respect to the $a$-mirror plane to the higher lying empty band formed from the same V-$d_{xy}$ orbitals but even with respect to that mirror plane, which explains its polarization and large oscillator strength. It is found both for the ferromagnetic and antiferromagnetic arrangement of the spins along the $b$ direction. We relate our main finding to a recent experimental study of cathodoluminescence (CL) in which a suppression of the lowest CL peak was observed upon addition of Li. Based on our and literature results, we present a different interpretation of the CL peaks from that study, which was based on the orbital character in a band-to-band picture. The lowest CL peak near 1.8 eV, which lies well below the indirect absorption onset of ${\mathrm{V}}_2{\mathrm{O}}_5$, is proposed to be related to recombination of a self-trapped electron polaron, resulting from oxygen vacancies, with a hole at the valence band maximum and is suppressed in ${\mathrm{LiV}}_2{\mathrm{O}}_5$ by the strong self-absorption from the Li induced occupied band to the higher empty bands at about the same energy.

$\mathrm{LaR}{\mathrm{u}}_3\mathrm{S}{\mathrm{i}}_2$ is a kagome superconductor with a relatively high superconducting transition temperature of $T_{\mathrm{c}}\approx 7.0\mathrm{K}$, making it a promising candidate for exploring the relationship between superconductivity and exotic electronic properties in a kagome lattice. We report on the superconducting properties of $\mathrm{LaR}{\mathrm{u}}_3\mathrm{S}{\mathrm{i}}_2$ through electrical resistivity, heat-capacity, and point-contact spectroscopy measurements. The temperature dependence of the upper critical field and low-temperature electronic specific heat is best described by single $s$-wave superconductivity. This conclusion is further supported by point-contact spectroscopy results, which, when analyzed by the modified Blonder-Tinkham-Klapwijk model, are consistent with the $s$-wave superconducting gap Δ. The evolution of Δ as a function of temperature and magnetic field follows the behavior characteristic of conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, with a zero-temperature value $\mathrm{\Delta }\left(0\right)$ of 1.2 meV. The gap-to-$T_{\mathrm{c}}$ ratio $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{c}}$ is 4.27, which is larger than the weak-coupling BCS value of 3.52, indicating that $\mathrm{LaR}{\mathrm{u}}_3\mathrm{S}{\mathrm{i}}_2$ belongs to the family of moderately coupled superconductors. These results can guide future research in understanding the enhancement of $T_{\mathrm{c}}$ and the underlying pairing mechanism in the geometrically frustrated systems.

Previously, it was believed that conduction and valence bands exhibit a symmetry: They possess opposite topological invariants (e.g., the Chern numbers of conduction and valence bands for the Chern insulator are $\pm C$). However, we present a counterexample: The second Stiefel-Whitney numbers for conduction and valence bands over the Klein bottle may be asymmetric, with one being nontrivial while the other trivial. Here, the Stiefel-Whitney classes are the characteristic classes for real Bloch functions under $PT$ symmetry with ${\left(PT\right)}^2=1$, and the Klein bottle is the momentum-space unit under the projective anticommutation relation of the mirror reflection reversing $x$ and the translation along the $y$ direction. The asymmetry originates from the algebraic difference of real cohomology classes over the Klein bottle and torus. This discovery is rooted in the foundation of topological band theory, and has the potential to fundamentally refresh our current understanding of topological phases.

In studying compensated semimetals, the two-band model has proven extremely useful in capturing electrical conductivity under magnetic field, as a function of density and mobility of electronlike and holelike carriers. However, it rarely offers practical insight into magnetothermoelectric properties. Here, we report the field dependence of thermoelectric (TE) coefficients in a highly compensated semimetal ${\mathrm{NbSb}}_2$, where we find the Seebeck ($S_{xx}$) and Nernst ($S_{xy}$) coefficients increase quadratically and linearly with applied magnetic field, respectively. Such field dependence was predicted in previous work that studied a system of two parabolic bands, within semiclassical Boltzmann transport theory when the following two conditions are simultaneously met: ${\omega }_c\tau \gg 1$ and $tan{\theta }_H\ll 1$, where ${\omega }_c$ and $\tau$ refer to the cyclotron frequency and relaxation time, respectively, and ${\theta }_H$ is the Hall angle. Under these conditions, we find the field dependence of the TE coefficients directly provides a relation between the electronlike ($n_e$) and holelike ($n_h$) carrier densities, which in turn can be used to refine two-band model fitting. With this, we find the compensation factor ($\frac{\left|\mathrm{\Delta }n\right|}{n_e}$, where $\mathrm{\Delta }n=n_e-n_h$) of ${\mathrm{NbSb}}_2$ is two orders of magnitude smaller than what was found in unrestricted fitting, resulting in a larger saturation-field scale for magnetoresistance. Within the same framework of the semiclassical theory, we also deduce that the thermoelectric Hall angle $tan{\theta }_{\gamma }=\frac{S_{xy}}{S_{xx}}$ can be expressed as $(\frac{\mathrm{\Delta }n}{n_e}\times {\omega }_c\tau {)}^{-1}$, which serves as a parameter to predict the degree of compensation. Our findings offer crucial insights into identifying empirical conditions for field-induced enhancement of TE performance and into engineering-efficient thermoelectric devices based on semimetallic materials.

The XY-plaquette model is the most straightforward lattice realization of a broad class of fractonic field theories that host quasiparticles with restricted mobility. The plaquette interaction appears naturally as a ring-exchange term in the low-energy description of exciton Bose liquids, cold atomic gases, and quantum dimer models. Using first-principle Monte Carlo simulations, we study the phase diagram and the vortex dynamics in the XY-plaquette model on a square lattice in two spatial dimensions. In its minimal formulation, the model contains a ring-exchange plaquette term in two spatial dimensions and a standard XY-link term in the (imaginary) time direction. We show that the phase diagram of the minimal XY-plaquette model possesses two phases: (i) a disordered vortex-dominated phase in which a single percolating vortex trajectory occupies the whole three-dimensional spacetime; (ii) a partially disordered phase in which the vortices become partially immobile, with their worldlines strictly confined to one or several infinite two-dimensional planes. The spatial positions and spatial orientations (along $x$ or $y$ axis) of these vortex domain walls appear to be spontaneous. Individual vortices form a disordered system within each vortex domain wall, so the fractal spacetime dimension of vortex trajectories approaches $D_f=2$. We argue that the appearance of the vortex walls could be interpreted as a consequence of the spontaneous breaking of a global internal symmetry in the compact XY-plaquette model.

We analyze the impact of spatial nonlocality and losses in the electromagnetic response of graphene on the Casimir-Lifshitz interaction. To this purpose, we calculate the Casimir-Lifshitz force (CLF) between a gold sphere and a graphene-coated ${\mathrm{SiO}}_2$ plane and compare our finding with the recent experiment in M. Liu et al. [Phys. Rev. Lett. 126, 206802 (2021) and Phys. Rev. B 104, 085436 (2021)]. We calculated the CLF using three different models for the electromagnetic response of graphene: electric conductivity using a nonlocal and lossy Kubo model, electric conductivity using the local and lossy Kubo model, and the nonlocal and lossless polarization operator model. The relation between these three models has been recently explored in P. Rodriguez-Lopez et al. [Phys. Rev. B 111, 115428 (2025)]. We show that, for the parameters of the available experiments, the theoretical predictions for the Casimir-Lifshitz force using the three models are practically identical (having relative differences smaller than ${10}^{-3}$). This implies that for those given experiments, both nonlocal and lossy effects in the graphene response are completely negligible. We also find that this experiment cannot distinguish between the Drude and Plasma prescriptions for the involved materials (gold and graphene). Our findings are relevant for present and future comparisons with experimental measurement of the Casimir-Lifshitz force involving graphene structures. Indeed, we show that an extremely simple local Kubo model for the electric conductivity, explicitly depending on Dirac mass, chemical potential, losses and temperature, is largely enough for a totally comprehensive comparison with typical experimental configurations. We also show how the Polarization tensor must be used and modified in general, for phenomena needing a more fine response function, i.e., requiring both the spatial nonlocality and losses.

We investigate the ground-state properties of the periodic Anderson model on the square lattice across various band fillings. Employing the infinite projected entangled-pair state (iPEPS) technique, we can determine the magnetic ground states accurately and compare them to mean-field predictions to highlight the effects of quantum fluctuations. At half filling, we analyze the transition between the antiferromagnetic and paramagnetic (Kondo singlet) phases as a function of hybridization and $f$-level energy, finding excellent agreement with existing quantum Monte Carlo studies in the case of hybridization. For $n=1.5$ electrons per site, we identify a correlated antiferromagnetic diagonal stripe phase as the ground state, which competes with its ferromagnetic partner state.

We consider the problem of Coulomb drag resistance in bilayers of electron liquids with spontaneously broken time-reversal symmetry. In the hydrodynamic regime, the viscosity tensor of such fluids has a nonvanishing odd component. In this scenario, fluctuating viscous stresses drive the propagation of plasmons, whose dispersion relations are modified by nondissipative odd viscous waves. Coulomb coupling of electron density fluctuations induces a drag force exerted by one layer on the other in the presence of a steady flow. This drag force can be expressed through the dynamic structure factor of the electron liquid, which is peaked at frequencies corresponding to plasmon resonances in the bilayer. As a result, the drag resistivity depends on the dissipationless odd viscosity of the fluid. We quantify this effect and present a general theory of hydrodynamic fluctuations applicable to odd electron liquids, both with and without Galilean invariance.

We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp, which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the Stückelberg oscillations in such a model for a ramp, which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent $\text{U}\left(1\right)$ symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.

Among the family of topological superconductors derived from ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Cu}}_x{\left(\mathrm{PbSe}\right)}_5{\left({\mathrm{Bi}}_2{\mathrm{Se}}_3\right)}_6$ is unique in its surface termination of a single quintuple layer (QL) of the topological insulator (TI) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ on an ordinary insulator PbSe. Here, we report a combined scanning tunneling microscopy (STM) and density functional theory (DFT) characterization of the cleaved surface of the parent compound ${\left(\mathrm{PbSe}\right)}_5{\left({\mathrm{Bi}}_2{\mathrm{Se}}_3\right)}_6$ (PSBS). Interestingly, the potential disorder due to the random distribution of native defects is only $\mathrm{\Gamma }\sim 4\mathrm{meV}$, comparable to the smallest reported for TIs. Performing high-resolution quasiparticle interference imaging (QPI) near the Fermi energy ($E-E_{\mathrm{F}}=-1$ to $0.6\mathrm{eV}$) we reconstruct the dispersion relation of the dominant spectral feature and our ab initio calculations show that this surface feature originates from two bands with Rashba-like splitting due to strong spin-orbit coupling and inversion symmetry breaking. Moreover, only a small hexagonal distortion of the calculated Fermi surface is seen in the full momentum space distribution of the measured scattering data. Nevertheless, the scattering pattern at lower energies transforms into a flowerlike shape with suppressed intensity along the $\overline{\mathrm{\Gamma }K}$ direction. We show that this effect is not due to the forbidden backscattering in the spin-momentum locked surface state in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ but reflects the threefold symmetry of the scattering potential.