We develop and systematically compare several analytical approximations for the ground state and zero-temperature polaron dispersion in finite-width, nonparabolic conduction bands. The main focus of the work is an extension of the Feynman variational method to a tight-binding lattice, where the effective-mass approximation is no longer applicable. The resulting variational formulation is not restricted to a specific phonon dispersion or electron-phonon interaction and provides a uniform description across weak-, intermediate-, and strong-coupling regimes. In addition, we revisit and generalize other analytical approaches traditionally formulated for continuum polarons, including canonical transformations and self-consistent Wigner-Brillouin-type approximations. For lattice polarons, these methods exhibit qualitative features absent in the continuum case, such as a nontrivial connection between weak- and strong-coupling limits. We show that an improved Wigner-Brillouin scheme yields a momentum-dependent polaron self-energy free of resonances and in good agreement with numerically exact results over the whole range of momenta within the Brillouin zone. All methods are applied to the Holstein model on a tight-binding lattice and are benchmarked against numerically exact calculations, including diagrammatic Monte Carlo (both our calculations and preceding works) and exact diagonalization results. Furthermore, the analytical approaches are extended to polarons with Rashba-type spin-orbit coupling, providing a stringent test of their applicability in systems with nontrivial band structure. Our results demonstrate that the modified Feynman variational method yields ground-state energies and dispersions with accuracy comparable to, and in many cases exceeding, that of other established analytical approaches. The developed framework offers a versatile and reliable analytical description of lattice polarons beyond the continuum approximation.

We present a pseudospin formulation for the postquench dynamics of charge-density-wave (CDW) order in the half-filled spinless Holstein model on a square lattice, assuming spatially homogeneous evolution. This Anderson pseudospin description captures the coherent nonequilibrium dynamics of the coupled electron-lattice system. Numerical simulations reveal three distinct dynamical regimes of the CDW order parameter following a quench—locked oscillations, Landau-damped dynamics, and overdamped relaxation—closely paralleling quench dynamics in Bardeen-Cooper-Schrieffer superconductors and other electronically driven symmetry-breaking phases. Crucially, however, the presence of dynamical lattice degrees of freedom leads to qualitatively different long-time behavior. In particular, while the oscillation amplitude is reduced in the damped regimes, CDW oscillations do not fully decay but instead persist for a long time due to feedback from the lattice field. We further show that these persistent oscillations are characterized by a nonequilibrium electronic distribution, which provides an intuitive understanding of both their amplitude and the renormalization of the oscillation frequency relative to the bare Holstein phonon frequency. Our results highlight the essential role of lattice dynamics in nonequilibrium ordered phases and establish a clear distinction between electron-lattice-driven CDW dynamics and their purely electronic counterparts.

We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For $B1$ (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp $4f$ quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-$4f$ electrons and the itinerant Ce-$5d$ and N-$2p$ electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order $B1$ → $B2$ (CsCl-type) transition with $\sim 11\%$ volume collapse in agreement with experiments. Across the transition, the $4f$ spectrum broadens, the $4f$ orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant $4f$ behavior. These features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

Since the discovery of phase transitions driven by topological defects, the classification of phases of matter has been significantly extended beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking (SSB). In particular, intrinsic and symmetry-protected topological (SPT) orders have been discovered in (mostly gapped) quantum many-body ground states. However, these are commonly viewed as zero-temperature phenomena, and their robustness in a gapless ground state or against thermal fluctuations remains challenging to tackle. Here we introduce an explicit construction for SPT-type states with hidden order associated with SSB: They feature (quasi-)long-range correlations along appropriate edges but short-range order in the bulk, ground state degeneracy associated with SSB, and nonlocal string order in the bulk. We apply our construction to predict two types of finite-temperature SPT transitions protected by 1-form symmetries in the Ising and BKT class, respectively, where the usual signs of criticality appear despite the absence of a diverging correlation length in the bulk. While the state featuring hidden Ising order is gapped, the other SPT state associated with the BKT-SPT transition has hidden $U\left(1\right)$ or XY order and constitutes an intrinsically gapless SPT state, associated with a gapless Goldstone mode. Specifically, in this work we discuss spins with global ${\mathbb{Z}}_2$ or $U\left(1\right)$ symmetry coupled to link variables constituting a loop gas model with a 1-form symmetry. By mapping this system to an Ising-gauge theory, we demonstrate that one of the SPT phases we construct corresponds to the Higgs-SPT phase at $T=0$ – which we show here to remain stable at finite temperature. Our work paves the way for a more systematic search for hidden order SPT phases, including in gapless systems, and raises the question if a natural (finite-$T$) spin liquid candidate exists that realizes hidden order in the Higgs-SPT class.

Quantum oscillations (QOs) are a well-established probe of Fermi-surface (FS) geometry and in the presence of long-range density wave order can display new QO frequencies from reconstructed FS pockets. We show that such reconstructed frequencies can arise even in the absence of long-range density order. Considering electrons coupled to a fluctuating bosonic mode that scatters quasiparticles between sharp hot spots on the FS, we develop a semiclassical theory in which the interaction generates time-dependent tunneling processes analogous to magnetic breakdown. This dynamical magnetic breakdown produces new semiclassical orbits corresponding to reconstructed FS areas despite the absence of static order. Because tunneling probabilities depend on the thermal population of bosonic excitations, the resulting oscillation amplitudes exhibit characteristic deviations from standard Lifshitz-Kosevich behavior. Our results provide a mechanism to probe bosonic fluctuations in quantum critical metals and provide a framework for dynamical magnetic breakdown.

We investigate photocurrent generation in undoped $\mathrm{GaAs}/\mathrm{A}{\mathrm{l}}_{0.3}\mathrm{G}{\mathrm{a}}_{0.7}\mathrm{As}$ multiple quantum wells at room temperature using spatially resolved photocurrent mapping. Under linearly polarized excitation, the response is dominated by the photothermoelectric effect. In contrast, helicity-dependent maps under circularly polarized light reveal two transverse spin-related contributions: a photoinduced anomalous Hall effect (PAHE) and a spin Nernst effect (SNE). With a transverse bias, spin-polarized carriers generated by circularly polarized light are transported in the presence of temperature gradients and converted to charge signals via the inverse spin Hall effect, producing photocurrent at the electrodes and within the device interior. The PAHE is consistent with spin-dependent deflection, whereas the SNE arises from thermally driven spin accumulation. Both contributions scale approximately linearly with the applied optical power over the measured ranges. These results clarify transverse spin transport in GaAs-based quantum wells and inform the design of III-V spintronic photodetectors.

We propose a symmetry-resolved optical probe of intrinsic loop-current chirality in moiré materials, with twisted bilayer graphene as a representative realization. Interlayer interference generates chiral electronic circulation on triangular plaquettes, giving rise to an intrinsic geometric chirality that enters the second-order response through a $C_3$-selected angular harmonic of the Berry curvature and can be isolated by the orbital-angular-momentum difference $\mathrm{\Delta }\ell$ of interfering optical vortex beams. When moiré $C_3$ symmetry is preserved, the intrinsic contribution appears in the $\mathrm{\Delta }\ell =3$ channel of the helicity-dependent dc photocurrent, whereas $C_3$-breaking perturbations activate additional channels. These results establish angular-momentum-resolved nonlinear optics as a route to probing geometric chirality in moiré and other symmetry-engineered quantum materials.

Transitions from bound states in the continuum (BICs) to quasi-BICs ($q\mathrm{BICs}$) are typically realized by introducing in-plane asymmetry, including permittivity asymmetry (ε-qBICs) and geometry asymmetry ($\mathrm{g}\text{−}q\mathrm{BICs}$). Here, we demonstrate that when the in-plane symmetry is rigorously kept, the transition can also occur, provided the out-of-plane asymmetry is designed, which is called ${\sigma }_h\text{−}q\mathrm{BICs}$ in this work. When the ${\sigma }_h$ symmetry is gradually broken and exceeds a certain threshold, the system undergoes a transition from BIC to qBIC. During the process, a topological phase transition characterized by a Zak phase inversion accompanied by a band inversion appears. This process not only enables controlled radiation coupling of BICs but also introduces a defect-immune $q\mathrm{BIC}$ regime. Our findings establish a general mechanism for engineering high-$Q$ resonances and topologically robust plasmonic cavities.

${\mathrm{TbMnO}}_3$ is a model type-II multiferroic where ferroelectricity appears with spiral magnetic order, but its microscopic origin remains unresolved. Utilizing novel approach using polarized Raman spectroscopy, we isolate individual Raman tensor and directly provide evidence of anionic displacements across the ferroelectric transition $\left({\mathrm{T}}_{\mathrm{FE}}\right)$, which is not possible by structural probes. The tensor element related to $c$ axis polarizability showed a sharp anomaly below ${\mathrm{T}}_{\mathrm{FE}}$. Quantitative analysis resulted in atomic displacement of ∼121 fm, in agreement with first-principles calculations, demonstrating that ferroelectricity in ${\mathrm{TbMnO}}_3$ is driven by atomic displacements.

We analyze thermally induced spin transport in $X$-wave magnets with $X=p,d,f,g$, and $i$. A prominent feature of $d$-wave altermagnets is that spin current is generated by applying a temperature gradient, which is known as the spin-Nernst effect. We show in $f$-wave magnets that spin current is generated proportional to the square of the temperature gradient, which we call the nonlinear spin-Seebeck current. It can be used as a spin current diode. In addition, we show in $g$-wave altermagnets that spin current is generated in the third order of the temperature gradient. We also show in $i$-wave altermagnets that spin current is generated perpendicular to the temperature gradient, which is the spin-Nernst current. We have derived analytic formulas for these spin currents. On the other hand, we show in $p$-wave magnets that spin current is not generated by temperature gradient.

The surface states of certain topological phases can be linked to a quantum anomaly: the violation of a classical symmetry by a field theory via a nonconserved current. This has been generalized to the case of a non-Hermitian (NH) chiral anomaly affecting the surfaces states of an NH Weyl phase. Here, we show that the NH anomaly inflow is mediated by continnum Landau modes (CLMs): special eigenstates exhibiting both spatial localization and a continuous spectrum, contrary to the usual distinction between bound and free states. The number of anomaly-induced surface modes scales with the sample volume rather than its surface area, which is shown to be tied to the unusual multiplicity of the CLMs. The other properties of the CLMs, including their normalization conditions and localization scale, closely match the predictions of the NH field theory. Finally, we discuss the conditions under which these phenomena can be probed experimentally using metamaterials.

Two-dimensional (2D) Dirac fermions occur ubiquitously in condensed matter systems from topological phases to quantum critical points. Since the advent of topological semimetals, where the dispersion is often tilted around the band crossing where the Dirac fermion can appear, tilt has emerged as a key handle that controls physical properties. We study how tilt affects the transport and spectral properties of tilted 2D Dirac fermions under scalar disorder. Although our spectral analyses always show conformity to appropriate Gaussian ensembles, suggestive of delocalization, the conductivity scaling $g\left(L\right)$ shows a surprising richness. For a single Dirac node, relevant for quantum Hall transitions and topological insulator surface states, we find $g\left(L\right)\sim a_{1}log\left(L\right)$ with a tilt-dependent coefficient $a_1>0$. Interestingly, when the tilt and transport directions are aligned, $a_1$ and hence $g\left(L\right)$ show a spike at the critical point between the type-I and type-II regimes of the Dirac node. For systems with two Dirac nodes with unbroken time-reversal symmetry, pertinent to quasi-2D Dirac materials, we find $g\left(L\right)\sim L^{a_1}{(logL)}^{a_2}$. However, we find a surprising tension between tilt along and perpendicular to the transport directions. For the former, $a_1$ changes sign as a function of tilt, hinting at a tilt-driven localization-delocalization transition, while $a_1<0$ for all tilts in the latter case, implying localization. These localized behaviors also reveal tension with the delocalization seen in spectral properties and suggest differing localization tendencies in real and Hilbert spaces. Overall, our work identifies tilt as an essential control parameter that uncovers rich and unconventional transport physics in 2D Dirac materials.

We study the growth and saturation of complexity in Krylov basis in random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, this notion of complexity grows linearly before saturating at a late-time value of $d/2$, where $d$ is the Hilbert space dimension, at timescales $\sim d$. Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits. In brick-wall case, complexity in the Krylov basis exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of the complexity enabling us to probe the transition between thermal and many-body localized phases.

Noncollinear antiferromagnets (NCAFs) offer an ideal platform for high-performance spintronic devices. Weak spin-orbit coupling (SOC) magnets, though abundant and important, are overlooked. We propose a symmetry framework for two-dimensional triangular antiferromagnets with ${120}^{\circ }$ spin configurations, exploring multi-degree-of-freedom coexistence, coupling, and manipulation in the weak SOC regime. Symmetry analysis reveals the spin chirality driven ferroelectricity, Berry curvature, and antiferromagnetic-induced spin splitting—beyond magnetic or spin space group descriptions—coupled via an inversion-induced spin-chirality transformation. The coexistence and coupling of these properties remain regardless of the in-plane rotation of ${120}^{\circ }$ spin configurations. Ferroelectric polarization reversal will switch spin chirality, Berry curvature, and spin splitting, enabling nonvolatile electric manipulation. Spin canting further breaks effective time-reversal symmetry, introducing unconventional SOC-independent valley polarization as an additional coupled degree of freedom. Multiple functionalities, including magnetoelectric coupling, circular dichroic Hall effect, nonrelativistic anisotropic Edelstein effect, and anomalous valley Hall effect, are enabled. High-throughput calculations on triangular-lattice MXenes identify monolayer ${\mathrm{Zr}}_2{\mathrm{VC}}_2{X}_2$ ($X=\text{F}$, Cl, Br, I) as promising candidates hosting ${120}^{\circ }$ spin configurations. First-principles calculations exemplified by ${\mathrm{Zr}}_2{\mathrm{VC}}_2{\mathrm{Cl}}_2$ validate the predicted tunability and multifunctionality. This work establishes a symmetry-guided framework for NCAF-based spintronic devices with tunable multifunctionality.

We theoretically investigate the effects of time-dependent electromagnetic fields on frustrated magnets with the spatial inversion symmetry. Two types of external-field setups are considered. One is a circularly polarized electromagnetic field and the other is a combination of a circularly polarized electric field and a static magnetic field. The system is modeled by a classical frustrated Heisenberg model on a triangular lattice, whose ground state is a single-$Q$ spiral spin configuration. The effects of irradiated electric and magnetic fields are taken into account by the inverse Dzyaloshinskii-Moriya (DM) interaction and the Zeeman coupling, respectively, without heating effects. By numerically solving the Landau-Lifshitz-Gilbert equation, we find that the two field configurations lead to distinct skyrmion crystal (SkX) phases and their associated topological phase transitions: in the former setup, SkXs composed of skyrmions with skyrmion numbers of one and two with opposite signs emerge, whereas in the latter setup, SkXs with the same sign appear. The stabilization mechanisms of these SkXs are accounted for by the competition among electromagnetic-field-induced chiral DM interactions, electric-field-induced three-spin interactions, and the Zeeman coupling based on the high-frequency expansion within the Floquet formalism. Furthermore, for the latter setup, we find that the stability region of the SkX phase varies significantly depending on the timing of the application of the circularly polarized electric field and the static magnetic field. Our findings would broaden the possible routes to generate and control SkXs by time-dependent electromagnetic fields, advancing both the theoretical comprehension and experimental control of topological spin crystals.

Despite numerous recent studies on the Hall anomaly following the discovery of cuprate superconductivity, its origin remains contentious. We demonstrate—without invoking adjustable parameters—that a previously proposed mechanism, in which vacancies form within vortex lattice domains, provides a compelling explanation for the observations in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_x$ thin films reported by Nitzav and Kanigel [Phys. Rev. B 107, 094516 (2023)]. In particular, the observed power-law behavior of ${\rho }_{xy}$ vs ${\rho }_{xx}$, with or without sign reversal, is consistent with the picture of vacancies on domains. Moreover, the effective vortex line length remains 1.5 unit cells (UC) across different experiments, independent of film thickness.

Using infrared and Raman spectroscopies combined with high-resolution x-ray diffraction, we address several controversial aspects of altermagnetic $\alpha$-MnTe. We show that mechanical stress applied to crystals of this material causes a drastic broadening of Bragg peaks that conceals signatures of additional phases present in the sample. Indeed, spatially resolved Raman spectroscopy reveals that the modes around $175{\mathrm{cm}}^{-1}$ often reported in $\alpha$-MnTe are not reproducible across different positions and samples and originate from the secondary phase of ${\mathrm{MnTe}}_2$. By combining spectroscopic probes with ab initio calculations, we establish the IR-active optical phonon of $\alpha$-MnTe around $155{\mathrm{cm}}^{-1}$ ($E_{1u}$) and the Raman-active optical phonon around $100{\mathrm{cm}}^{-1}$ ($E_{2g}$) at room temperature. Two intense Raman modes around 120 and $140{\mathrm{cm}}^{-1}$ are shown to be intrinsic, even though they can not be assigned to $\mathrm{\Gamma }$-point optical phonons. These modes couple to magnetic order in $\alpha$-MnTe and also to the transient reflectivity, resulting in coherent oscillations. Both sixfold rotation symmetry and inversion symmetry are preserved in bulk $\alpha$-MnTe within our experimental resolution.

The determination of the mobility edge (ME)—the critical energy threshold separating extended and localized quantum states—remains a central challenge in the study of Anderson transitions, particularly within complex non-Hermitian systems where conventional Hermitian techniques often fail. While the standard Aubry–André–Harper model provides a paradigmatic example of localization in one-dimensional quasiperiodic systems, the precise analytical determination of MEs in models breaking standard self-duality has proven elusive. This comprehensive report presents a rigorous and exhaustive theoretical framework for a class of non-Hermitian quasiperiodic network models that incorporate both periodic and quasiperiodic sublattices, nonreciprocal hopping, and complex quasiperiodic potentials. By systematically integrating out periodic degrees of freedom, we unveil a “hidden” self-duality in the effective Hamiltonian, a symmetry absent in the original description. We derive exact, energy-dependent MEs defined by the effective potential $g\left(E\right)V$ and eigenenergy $f\left(E\right)$. We demonstrate that states satisfying $g\left(E\right)=0$ are intrinsically extended, allowing for the precise analytical prediction of ME trajectories. Furthermore, we generalize this duality-based approach to systems exhibiting nonuniform (Su–Schrieffer–Heeger type) and long-range (exponentially decaying) hopping. This work not only provides exact analytical solutions for a broad class of previously intractable models but also offers a unifying perspective on the interplay between non-Hermiticity, topology, and quasiperiodic disorder, with significant implications for experimental realizations in photonic and acoustic metamaterials.