Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features governing the critical transition remains elusive in many disordered and quasirandom systems. In this study, we explore the ergodic-to-many-body localization transition in the generalized Aubry-André model with interacting spinless fermions. Using the concept of Frobenius norm of an adiabatic gauge potential, we construct a phase diagram that captures the sensitivity of the eigenspectrum to infinitesimal adiabatic gauge deformations. To examine the stability of the critical disordered strength with respect to system size, we perform an unbiased finite-size scaling analysis via cost-function minimization techniques. Additionally, by analyzing the adjacent gap ratio and spectral form factor, we determine the scaling behavior of the Thouless time as a function of the disorder strength.

We report a systematic study of spin and charge ordering in cubic perovskites ${\mathrm{Ba}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ ($0.1\le x\le 0.5$) obtained by high-pressure syntheses. On the basis of detailed magnetic measurements including Mössbauer spectroscopy, a previously unreported spin-charge correlated phase is found to emerge around $x=0.2$ as an intermediate phase between the helimagnetic phase near $x=0$ and the commensurate spin-charge ordered phase around $x=1/3$. Mössbauer spectra measured at low temperatures reveal that the charge disproportionation, expressed as $2{\mathrm{Fe}}^{(4-x)+}\to (1+x){\mathrm{Fe}}^{3+}+(1-x){\mathrm{Fe}}^{5+}$, takes place over a wide range of the helimagnetic phase, from around $x=1/3$ down to 0.1, where long-range ordering of charge disproportionation is disturbed presumably by the incommensurate helimagnetic order. This work reveals strong charge disproportionation instability potentially coupling with helical spin ordering in ${\mathrm{Fe}}^{4+}$-based perovskite oxides.

Two-dimensional (2D) triferroic materials, which simultaneously host ferroelectric, ferromagnetic, and ferrovalley orders, are regarded as ideal platforms for developing next-generation nonvolatile multistate memory devices. However, achieving coupling among these order parameters, stability above room temperature, and their coexistence with higher-order topology in an intrinsic monolayer remains challenging. Based on first-principles calculations, we predict that monolayer ${\mathrm{TcIrGe}}_2{\mathrm{Se}}_6$ (TIGS) is an intrinsic 2D triferroic semiconductor stable above room temperature. Specifically, this system possesses switchable out-of-plane ferroelectric polarization and polarization-controllable valley polarization, together with a ferromagnetic ground state stabilized by the supersuperexchange mechanism, with a Curie temperature reaching 405 K. More importantly, pronounced coupling among ferroelectric order, magnetic order, and valley physics is found in TIGS. As a result, polarization reversal modulates the magnetic interactions, reverses both the sign of the valley splitting and the DMI chirality, and modulates Berry-curvature-related transport responses. In addition, TIGS exhibits higher-order topological characteristics and supports a long-range-ordered skyrmion lattice. These results identify TIGS as a promising platform for exploring the cooperative interplay among 2D multiferroic coupling, higher-order topology, spin textures, and valley physics.

Kagome metals exhibit diverse exotic phenomena, including superconductivity, nontrivial electronic topology, and charge-density wave (CDW) states. Here, we demonstrate that photoenhanced superconductivity and topological phonons emerge after the CDW order is suppressed via optical excitation in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. Real-time time-dependent density-functional theory simulations demonstrate that laser irradiation leads to a complete suppression of CDW order with the photocarrier density of ∼0.18 electrons per formula unit. Consequently, the calculated superconducting critical temperature increases to 7.3 K in the high-symmetry phase stabilized by photoexcitation and subsequently decreases with stronger electronic excitation. In addition, the high-symmetry phase hosts nontrivial topological phonons. This work offers more insights for understanding photoinduced superconductivity and phonon topology, stimulating future investigations into the nonequilibrium properties of kagome materials, with broad implications for topological superconductivity and coupled quantum electron-phonon devices.

Supervised machine learning can help learn topological invariants for topological systems. However, it faces severe limitations when applied to non-Hermitian topological phases. The nonlinear nature of the non-Bloch topological invariant causes a sudden change in non-Hermitian or high-dimensional situations, while supervised machine learning does not have the ability to grasp the rule at this moment. We have rigorously demonstrated the limitation of supervised machine learning and systematically delineated the valid scale range for effective model predictions through generalization error bounds. By integrating the hypothesis space and the underlying physical mechanisms, our work establishes a generalized theoretical framework for evaluating the feasibility of supervised machine learning in topological phase identification.

Uniaxially strained Fe-Co disordered alloys have emerged as promising candidates for cost-effective (especially Fe-rich alloy), high Curie temperature (both Fe-rich and Co-rich), rare-earth-free permanent magnets due to their high magnetocrystalline anisotropy energy (MAE). Using first-principles, fully relativistic calculations within the coherent potential approximation and Perdew-Burke-Ernzerhof exchange-correlation potential, we explore the MAE of tetragonal Fe-Co alloys under uniaxial compression. Our results reveal a previously uncharted region of high MAE (exceeding $3\mathrm{MJ}{\mathrm{m}}^{-3}$) accessible via uniaxial compression. This phase, which lies between hexagonal-close-packed and body-centered-cubic structures, exhibits a high magnetic moment and Curie temperature, and thus offers a more stable candidate for experimental realization than the currently known high-MAE uniaxially strained Fe-Co.

We investigate the temperature-dependent magnetic phase evolution in the van der Waals layered magnet ${\mathrm{Fe}}_{4.5}{\mathrm{GeTe}}_2$ using static magnetometry and broadband ferromagnetic resonance (FMR) spectroscopy. Below the Curie temperature ($T_{\mathrm{C}}\approx 270\mathrm{K}$), ${\mathrm{Fe}}_{4.5}{\mathrm{GeTe}}_2$ exhibits a sophisticated sequence of magnetic transitions. Static magnetization measurements identify anomalies at ∼180 and ∼100 K, indicating a departure from a simple collinear ferromagnetic ground state. Temperature-dependent FMR spectra reveal a crossover from a dominant single resonance to two dynamically distinct in-plane branches below approximately 180 K. The prominent high-field branch exhibits Kittel-like frequency-field behavior and is consistent with the approximately uniform precession of the field-polarized net magnetization, whereas the additional low-field branch may be associated with canted or spatially nonuniform magnetic components. Below approximately 100 K, the spectra become strongly broadened and multimode, indicating an increasingly nonuniform magnetic response without allowing a unique microscopic mode assignment. The temperature-driven anisotropy crossover is quantitatively tracked through the evolution of the magnetocrystalline anisotropy field, effective magnetization, and $g$-factor anisotropy. The anisotropic $g$-factor and its deviation from the free-electron value are consistent with an appreciable orbital and spin-orbit-coupling contribution associated with the reconstructed magnetic response. Our findings establish $\mathrm{F}{\mathrm{e}}_{4+\delta }\mathrm{GeT}{\mathrm{e}}_2$ as a platform for exploring anisotropy-controlled spin dynamics and nontrivial magnetic phases in high-$T_{\mathrm{C}}$ two-dimensional magnets.

Magnetic skyrmions are topological quasiparticles potentially useful for memory and computing devices. Antiferromagnetic (AF) skyrmions present no transverse deflection, making them suitable candidates for data storage applications. After the discovery of skyrmions with length scales comparable to the lattice constant, several works presented quantum analogs of classical ferromagnetic skyrmions in spin systems. However, studies about quantum analogs of AF skyrmions are still lacking. Here, we explore the phases of the AF quantum spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interactions on the triangular lattice using the density matrix renormalization group algorithm. We study the magnetization profile, spin structure factor, and quantum entanglement of the resulting ground states to characterize the corresponding phases and signal the emergence of quantum AF skyrmions. Moreover, we present calculations of the quantum analogs of the scalar chirality, and construct local chirality maps, to further explore the different phases. Our results support that three-sublattice quantum antiferromagnetic skyrmion textures are stabilized in a wide range of magnetic fields.

In [S. Ansari et al., Phys. Rev. B 112, 054304 (2025)], dynamical quantum phase transitions (DQPTs)—nonanalyticities in the Loschmidt return rate at critical times—are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. The protocol used approximates the noise-averaged mixed state, obtained using a master equation, by a pure state, characterized by its excitation probability. In this comment we rigorously show that: (i) This approximation is exponentially poor in the thermodynamic limit. (ii) When using the correct metric, the Loschmidt echo of two density matrices in any two-dimensional Hilbert space can become zero if and only if both density matrices are pure, ruling out DQPTs for nonzero noise. (iii) An a posteriori reinterpretation of the results as an interferometric protocol is possible but such a protocol is unsuitable to investigate the effects of noise on DQPTs because it is inherently blind to decoherence. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.

The Comment by Sirker [arXiv:2511.16509] raises an important issue concerning dynamical quantum phase transitions (DQPTs) in noisy and mixed-state dynamics, namely that the extension of the Loschmidt echo from pure to mixed states is not unique and different extensions preserve different physical properties. The Comment examines a noise-averaged mixed-state fidelity and shows that, DQPTs cannot occur for any nonzero noise when the return rate is defined through the Uhlmann-Bures fidelity of the noise-averaged density matrix. This conclusion is valid for the mixed-state fidelity observable discussed in the Comment and is consistent with prior studies [Jafari, Langari, Eggert, and Johannesson, Phys. Rev. B 109, L180303 (2024); Jafari, Akbari, Biderang, and Sirker, arXiv:2504.03005]. Our article [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)] investigated a different operationally defined quantity: the logarithm of the Loschmidt echo obtained by first determining the noise-averaged excitation probabilities generated during the noisy ramp and then performing a coherent postramp evolution of a pure state constructed from these noise-averaged transition probabilities. As emphasized explicitly in our original publication, this observable is defined through an operational assumption and is not the same quantity as the mixed-state fidelity. The nonanalyticities reported in [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)], therefore, concern this two-stage operational protocol and should not be identified with zeros of the Uhlmann-Bures fidelity. There is, therefore, no direct contradiction between the theorem established for the Uhlmann-Bures return rate and the conclusions obtained for the different operational protocol studied in [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)].

We report a high-pressure study of superconductivity and structural evolution in the layered Zintl compound $6R-\mathrm{CaG}{\mathrm{e}}_2$. Upon compression, $\mathrm{CaG}{\mathrm{e}}_2$ undergoes two successive structural transitions, from $R\text{−}3m$ to $P\text{−}3m1$ at 7.5 GPa and then to $P$-1 at 30.4 GPa. Superconductivity emerges near 16 GPa in the $P\text{−}3m1$ phase with $T_{\mathrm{c}}\sim 3$ K; $T_{\mathrm{c}}$ then shows an initial increase followed by a nearly pressure-independent plateau. A second superconducting state appears near the onset of the $P$-1 phase, where $T_{\mathrm{c}}$ reaches $\sim 7$ K and is gradually suppressed upon further compression. Upon decompression, $T_{\mathrm{c}}$ in the $P$-1 phase increases as the Debye temperature decreases, highlighting the important role of lattice dynamics. First-principles calculations indicate that the contrasting $T_{\mathrm{c}}$ evolution in the two high-pressure phases arises from phase-dependent electron-phonon coupling. In $P\text{−}3m1$, superconductivity is mainly associated with the reorganization and softening of low-frequency acoustic modes, whereas in $P$-1, $T_{\mathrm{c}}$ suppression arises from phonon hardening and a reduced electronic density of states at the Fermi level. Our results show that pressure-driven structural evolution in $\mathrm{CaG}{\mathrm{e}}_2$ reshapes electronic states and lattice dynamics, leading to phase-dependent superconductivity and providing insight into pressure-tuned superconductivity in layered Zintl compounds.

${\mathrm{LaCuS}}_2$ is a Cu-based rare-earth chalcogenide semiconductor whose structural robustness and pressure-dependent electronic evolution remain largely unexplored. Here, we investigate its structural, optical, and transport properties under compression by combining high-pressure experiments with first-principles calculations. ${\mathrm{LaCuS}}_2$ retains its monoclinic $P{2}_1/c$ structure up to 70.1 GPa without the emergence of a phase transition. Nevertheless, compression induces subtle local structural reorganization, including Cu-site disordering-to-ordering and an anisotropic lattice anomaly near 5.0 GPa associated with flattening of the corrugated corner-sharing ${\mathrm{Cu}}_2{\mathrm{S}}_6$ layers. Concurrently, the optical band-gap decreases continuously from 2.39 to 0.93 eV upon compression to 48.6 GPa, accompanied by distinct piezochromism and a progressive redshift of the photoluminescence emission. First-principles calculations reveal that the band-gap narrowing originates from the continuous evolution of the Cu $3d\text{−}\mathrm{S} 3p$ derived valence states and La $5d$ derived conduction states under compression. Electrical transport measurements show that ${\mathrm{LaCuS}}_2$ remains semiconducting up to 64.1 GPa, while photocurrent retains the same polarity throughout the investigated pressure range. These results establish ${\mathrm{LaCuS}}_2$ as an unusual pressure-robust semiconductor in which substantial band-edge engineering is achieved through continuous local structural evolution without a phase transformation, providing a model system for exploring pressure-induced electronic tuning in Cu-based rare-earth chalcogenides.

We demonstrate that wave amplification enables even weak nonlinearities to reshape linear wave-packet transport in nonreciprocal systems. We study the dynamics of bulk Gaussian wave packets in the Hatano- Nelson model with on-site cubic nonlinearity. We show that the interplay between nonlinearity and amplification generates growing frequency shifts that drive the wave packet through three successive dynamical regimes: an early nonlinear-skin regime with coherent propagation, an intermediate wave-mixing regime driven by eigenmode resonances, and a self-trapping regime in which part of the packet localizes while the remainder ballistically spreads along the system's favored direction. The crossover timescales are set by the width and averaged spacing of the eigenfrequency spectrum. Crucially, within the nonlinear-skin regime, we derive analytical predictions for the wave-packet dynamics and show that nonlinearity couples amplification, dispersion, and nonreciprocity, thereby modifying the magnitude of the wave-packet acceleration and introducing an explicit time dependence into its evolution. Focusing nonlinearities suppress the acceleration and cause it to decrease in time, whereas defocusing nonlinearities enhance it and cause it to increase. We further show that nonlinear interactions typically break down the wave packet before the non-Hermitian jump can occur. Our results provide a route toward accurate control of waves in nonreciprocal metamaterials.

A quantum anomalous Hall system is predicted to realize topological superconductivity when proximity coupled to an $s$-wave superconductor. A kagome magnet with chiral magnetic ordering exhibits the quantum anomalous Hall effect; however, superconducting proximity to an ordinary $s$-wave superconductor fails to induce pairing in the strong exchange coupling limit. In this work, we demonstrate that proximity coupling to a Rashba superconductor gives rise to topological superconducting phases characterized by odd Bogoliubov-de Gennes Chern numbers. We confirmed their consistency with the chiral central charge calculated based on the modular commutator. We also show that the magnetic ordering of kagome magnets is affected energetically by the proximity effect.

Stabilizing unconventional coordination environments in extended solids remains challenging, particularly for late transition metals such as gold (Au) with limited valence flexibility. Here, we report that a site-selective framework enables the formation of octahedral Au-S coordination in layered ${\mathrm{AuBS}}_3$, a structure related to quasi-$1T$ transition-metal dichalcogenides. Under compression, electron-deficient ${\mathrm{B}}_2{\mathrm{S}}_6$ units constrain the sulfur sublattice and modify the local ligand field, driving Au into an octahedral coordination environment. Electronic structure analysis shows that this framework lowers the energy of Au–S bonding states through overlap between S $3s/3p$ orbitals and Au $6s/6p$ as well as bonding $5d$ ($5d_{yz}$ and $5d_{xz}$) states, while leaving the remaining Au $5d$ ($5d_{xy}, 5d_{x^2\text{−}{y}^2}$, and $5d_{z^2}$) orbitals to largely retain their nonbonding character, thereby stabilizing the octahedral configuration beyond conventional valence constraints. As a consequence, ${\mathrm{AuBS}}_3$ exhibits intrinsic superconductivity, primarily originating from the strong electron-phonon coupling between Au–S antibonding electrons and low-frequency vibrations associated with Au–S bonds. These results highlight the role of framework-constrained bonding reconstruction in stabilizing unconventional coordination geometries and provide insight into the design of transition-metal chalcogenides under pressure.

It is generally believed that the spin-$\frac{1}{2}$ triangular-lattice $J_1-J_2$ Heisenberg model hosts a quantum spin liquid in the intermediate regime between the ${120}^{\circ }$ and stripe ordered phases. Density matrix renormalization group studies on cylinders have consistently found two nearly degenerate ground states, commonly interpreted as distinct topological sectors. Using state-of-the-art matrix product state simulations on YC6 cylinders, we compare the static and dynamical properties of these two sectors at $J_2/J_1=0.125$. Noticeable differences appear already in static correlations; moreover, high-resolution dynamical structure factors reveal qualitatively distinct low-energy excitations. These results suggest that the two ground states cannot be understood as merely topologically distinct sectors of a gapped ${\mathbb{Z}}_2$ spin liquid.

Based on a renormalization group (RG) analysis, we study the bosonization formulas for spin-$S$ Kitaev-Gamma and Kitaev-Heisenberg-Gamma chains in the parameter regime $K<0, \mathrm{\Gamma }>0$, and $J>0$, with $S$ being a half-odd integer. We find that the effects associated with the breaking of emergent continuous symmetries in the bosonization formulas scale as $1/S$ in the large-$S$ limit, in qualitative agreement with density-matrix renormalization group results for Kitaev-Gamma chains. For Kitaev-Heisenberg-Gamma chains, the low-energy excitations are characterized by incommensurate gapless wave vectors, and symmetry analysis yields ten independent bosonization coefficients, five of which are predicted by the RG analysis to be independent of the Heisenberg coupling up to linear order. Our results provide useful input for determining magnetic ordering tendencies in two-dimensional Kitaev spin models within a quasi-one-dimensional approach.

Sondheimer oscillations (SO) are magnetoresistance oscillations occurring in thin films due to the commensurability between cyclotron motion and sample thickness, and are traditionally regarded as a purely semiclassical size effect. Here we develop a general quantum theory of SO for thin-film conductors in the quantum limit of a large magnetic field. We show that corrections arising from band topology modify the SO frequency, in contrast to Shubnikov–de Haas oscillations where topological information appears only in the phase. As a consequence, quantum SO provide a direct and robust probe of the full Landau level spectrum. Applying our framework to a minimal model with tunable Berry phase, we demonstrate how topology manifests itself in experimentally accessible magneto-oscillation spectra and discuss damping mechanisms including surface roughness.