Integrable Trotterization provides a method to evolve a continuous-time integrable many-body system in discrete time, such that it retains its conserved quantities. Here, we explicitly show that the first-order Trotterization of the critical transverse-field Ising model is integrable. The discrete-time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using the quantum inverse scattering method. The inhomogeneity parameter determines the discrete-time step. We then focus on the noninvertible Kramers-Wannier duality symmetry for the Trotterized evolution. We find that the discretization of both space and time leads to a doubling of these duality operators. They account for discrete translations in both space and time. As an interesting application, we find that these operators also provide maps between Trotterizations of different orders. This helps us extend our results beyond the Trotterization scheme and investigate the Kramers–Wannier duality symmetry for finite-time Floquet evolution of the critical transverse-field Ising chain. Finally, we investigate how these noninvertible operators shape the phase diagram of the discrete-time evolution. This question is particularly interesting in the Floquet setting, which is known to host a richer phase structure than its undriven counterpart. We systematically construct the necessary operators, which relate different phases away from criticality for both Trotterized and Floquet evolutions.

Magnetic proximity effects in $\text{Co}\text{/}\text{hBN}\text{/}\text{graphene}$ heterostructures are systematically analyzed via first-principles calculations, demonstrating a pronounced localized spatial variation of the induced spin polarization of graphene's Dirac states. The proximity-induced exchange coupling, magnetic moments, and tunneling spin polarization (TSP) are shown to depend sensitively on the atomic registry at the interfaces. We analyze more than 20 distinct stackings—including high- and low-symmetry configurations—and reveal that the spin splittings of graphene's Dirac bands span a wide range from 1 to 100 meV, depending on the local hybridization of Co $d_{z^2}$, hBN $p_z$, and graphene $p_z$ orbitals. The strongest proximity effects emerge at geometric resonances, or “proximity hot spots”, where the three orbital states overlap maximally. The local spin polarization also depends sensitively on energy: Dirac states aligned with resonant Co orbitals experience the most pronounced exchange interaction. At these energies, the pseudospin Hamiltonian description of magnetic proximity effects breaks down. Outside these resonances, the pseudospin picture is restored. Our findings highlight the intrinsically local nature of proximity effects, governed by the spectral resonance and interlayer wave function overlap. We further quantify how additional hBN layers, interlayer twist, and multilayer graphene modify the proximity exchange and TSP, offering microscopic insight for designing spintronic van der Waals heterostructures with engineered interfaces and optimized spin transport.

Low-dimensional quantum systems host a variety of exotic states, such as symmetry-protected topological ground states in spin-1 Haldane chains. Real-world realizations of such states could serve as practical quantum simulators for quantum phases if the interactions can be controlled. However, many proposed models, such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, require unconventional forms of spin interactions beyond standard Heisenberg terms, which do not naturally emerge from microscopic (Coulomb) interactions. Here, we demonstrate a general strategy to induce a biquadratic term between two spin-1 sites and to tune its strength $\beta$ by placing pairs of spin-1/2 spacers in between them. $\beta$ is controlled by the ratio of the Heisenberg couplings between the spin-1 sites and the spacer spins, and between the spacer spins themselves. Detailed atomistic calculations reveal that chains of nanographene flakes with 22 and 13 atoms, respectively, which could be realized by state-of-the-art bottom-up growth technology, yield precisely the couplings required to approach the AKLT state. These findings deliver a blueprint for engineering unconventional interactions in bottom-up synthesized quantum simulators.

The altermagnet (AM), a recently identified class of collinear magnet, has garnered significant attention due to its unique combination of zero net magnetization and spin-split energy bands, leading to a variety of novel physical phenomena. Using numerically exact lattice Monte Carlo simulations, we investigate AM-like phases within the Ising-Kondo lattice model (the anisotropic easy-axis limit of the Kondo lattice model), which is commonly employed to describe heavy-fermion materials. By incorporating an alternating next-nearest-neighbor hopping (NNNH) term, which arises from the influence of nonmagnetic atoms in altermagnetic candidate materials, our results reveal key signatures of AM-like states, including spin-splitting quasiparticle bands and spectral functions, and demonstrate that a $d$-wave AM remains stable across a broad range of interaction strengths, electron concentrations, NNNH amplitudes, and temperatures, highlighting its robustness. Furthermore, through an analysis of non-magnetic impurity effects, we further confirm the $d$-wave symmetry of the AM phase. These findings establish a solid theoretical foundation for exploring AM-like phases in $f$-electron compounds, paving the way for future investigations into their exotic magnetic and electronic properties.

Moiré materials with opposite nonzero minibands Chern numbers in time-reversal-partner valleys are two-dimensional topological insulators at band filling $\nu =2$. We explore the possibility that in this class of moiré materials intervalley coherence can sometimes be present in interaction-induced insulators at band filling $\nu =1$, using Landau levels with opposite signs of the magnetic field as a convenient generic model. In the absence of intravalley interactions the mean-field ground state at filling factor $\nu =1$ is a gapless intervalley coherent state that maps under a particle-hole transformation of one valley to a strong-field superconducting vortex-lattice state that has been studied previously. When the ratio $\lambda$ of intravalley to intervalley exchange interactions is increased, gapped states appear, one with broken time-reversal symmetry and a quantized Hall effect but no valley polarization and one with broken parity symmetry and zero Hall conductivity. We discuss the possibility that the latter state could be related to the fractional quantum spin Hall effect recently observed at an odd filling factor in a moiré topological insulator and comment on related systems in which correlations between electrons in bands with opposite Chern numbers might play a key role.

Two-dimensional type-II topological semimetals (TSMs), characterized by strongly tilted Dirac cones, have attracted intense interest for their unconventional electronic properties and exotic transport behaviors. However, rational design remains challenging due to the sensitivity of band tilting to lattice geometry, atomic coordination, and symmetry constraints. Here, we present a bottom-up approach to engineer ideal type-II nodal line semimetals (NLSMs) in van der Waals bilayers via atomic intercalation. Using monolayer $h$-AlN as a prototype, we show that fluorine-intercalated bilayer AlN (F@BL-AlN) hosts a symmetry-protected type-II nodal loop around the $E_F$, enabled by preserved mirror symmetry $\left({\mathcal{M}}_z\right)$ and tailored interlayer hybridization. First-principles calculations reveal that fluorine not only tunes interlayer coupling but also aligns the Fermi energy with the nodal line, stabilizing the type-II NLSM phase. The system exhibits tunable electronic properties under external electric and strain fields and features a Van Hove singularity that induces spontaneous magnetism, undergoing a transition from a type-IV antiferromagnetic metal to a ferromagnetic topological semimetal with increasing strain. This work provides a versatile platform for designing type-II NLSMs and offers practical guidance for their experimental realization.

The orbital Hall effect has emerged as a fundamental phenomenon in the burgeoning field of orbitronics, offering a robust paradigm for the generation and manipulation of orbital angular momentum. Particularly, two-dimensional valleytronic materials have emerged as highly promising platforms for investigating this effect. Concurrently, Floquet engineering via periodic optical driving provides a powerful nonequilibrium pathway to dynamically control topological quantum states. In this work, we employ Floquet theory to investigate the band topology and the corresponding evolution of orbital transport in a gapped graphenelike model driven by circularly polarized light, aiming to dynamically tune both the magnitude and sign of the orbital angular momentum. We reveal that the interplay between the optical field and intrinsic spin-orbit coupling (SOC) fundamentally reshapes the topological phase transitions. Specifically, SOC functions as a spin-valley-dependent mass correction that breaks the synchronization of photoinduced band inversions. This desynchronization drives the system into a unique mixed topological phase, where only a single spin band within a specific valley undergoes band inversion. Consequently, the orbital transport exhibits a pronounced spin-valley coupled character: within the same valley, the Berry curvature and orbital magnetic moment for the two spin channels acquire opposite signs, leading to highly tunable, valley-resolved orbital angular momentum transport. By further evaluating the orbital Hall angle, we demonstrate that a giant orbital Hall angle emerges in the vicinity of the insulating gap due to the suppression of longitudinal charge transport. Compared with bulk transition metals, this gap-engineered feature provides a more favorable platform for the study and manipulation of orbital angular momentum transport.

We develop a microscopic theory of magnon-exciton drag effect in a bilayer van der Waals antiferromagnetic semiconductor CrSBr. Effective exciton-magnon coupling arises from an orbital mechanism: Magnons tilt the layer magnetizations, enabling charge carrier tunneling that mixes intralayer and interlayer excitons and thereby modulates the exciton energy. We derive the effective Hamiltonian of exciton-magnon coupling, based on our calculation of the magnon spectrum taking into account short-range exchange interaction between Cr-ion spins, single-ion anisotropy, and long-range dipole-dipole interactions. We show that despite rather small renormalization of exciton's energy and effective mass by the exciton-magnon interaction, the three key two-magnon processes, exciton-magnon scattering, two-magnon absorption by an exciton, and two-magnon emission, are highly efficient. By solving the Boltzmann kinetic equation, we evaluate a short exciton-magnon scattering time which is in the sub-ps range and strongly decreases with the increase in magnon population. Hence, exciton-magnon scattering is likely to be dominant over other scattering processes related to exciton-phonon and exciton-disorder interactions. We demonstrate that nonequilibrium magnons can efficiently drag excitons, resulting in a large and nearly isotropic exciton propagation that can significantly exceed the intrinsic anisotropic diffusion. Our results provide a theoretical basis for recent observations of anomalous exciton transport in CrSBr [F. Dirnberger et al., Nat. Nanotechnol. 21, 65 (2026)] and establish magnon-exciton drag as a powerful mechanism for controlling exciton propagation in magnetic systems.

Alternative theories of quantum statistics provide an avenue for exploring novel physics beyond bosons and fermions, yet experimental verification of their existence in nature proves a challenging task. Among these theories, it has recently been suggested that $R$ parastatistics can be realized as quasiparticle excitations in many-body systems. In this paper, we build on this idea by showing that signatures of $R$ parastatistics can be observed as flavor-charge separation in one-dimensional (1D) systems. We consider a generalized version of the Luttinger model (LM) and show that bosonization persists when the $R$ paraparticles have fermi-surface-like structures. These $R$ parafermions can satisfy generalized exclusion principles beyond conventional Pauli's. We show that density waves of all $R$ parafermions can always be bosonized, but flavor waves act like bosons only for a certain subclass of $R$ parafermions. We derive the conditions for bosonization by analyzing the LM spectrum, showing that bosonization applies only to low-temperature systems. Signatures of flavor-charge separation then become apparent as distinct dispersion profiles when we turn on interparticle interactions. This points to potential observations of flavor-charge separation in 1D systems that host emergent $R$ paraparticles.

We demonstrate an alternative approach based on a complex-valued inverse temperature and partition function to probe quantum phases of matter with nontrivial spectra and dynamics. It leverages thermofield dynamics (TFD) to quantitatively characterize quantum and thermal fluctuations, and exploit the correspondence between low-energy excitations and Fisher zeros. Using the quantum XY chain in an external field as a test bed, we show that the oscillatory gap behavior manifests as oscillations in the long-time dynamics of the TFD spectral form factor. We also identify giant bubbles, i.e., large-scale closed lines, of Fisher zeros near the gapless XX limit. They provide a characteristic energy scale that seems to contradict the predictions of the low-energy theory of a featureless Luttinger liquid. We identify this energy scale and relate the motion of these giant bubbles with varying external field to the transfer of spectral weight from high to low energies. The deep connection between Fisher zeros, dynamics, and excitations opens up promising avenues for understanding the unconventional gap behaviors in strongly correlated many-body systems.

The geometry of a physical system is intimately related to its spectral properties, a concept colloquially referred to as “hearing the shape of a drum.” Three-dimensional topological insulator nanowires in a strong magnetic field $B$ generally host Dirac-type quantum Hall (QH) surface states. The surface itself is shaped by spatial variations of the wires' cross section, yielding a curved geometrical background, the “drum,” with imprints in the corresponding QH spectra. We show that the latter are composed of two different classes. The first one is asymptotically insensitive to the surface shape, scaling as $B^{1/2}$, like regular planar QH states. Instead, the second has an asymptotic $B$-field dependence intimately related to the wire geometry. We further demonstrate that an (axial-symmetric) curved nanowire surface possesses a reciprocal partner surface, such that the respective QH spectra are dual to each other upon exchanging angular momentum and magnetic flux. Notably, a cone-shaped nanowire, and the Corbino geometry as its limiting case, has a reciprocal partner with a dual QH spectrum that is $B$-field independent, with corresponding nonmagnetic QH-type states. We support our analytical findings by numerical results for $B$-field ranges and wire geometries within reach of current experiment.

As emerging ferroelectric (FE) materials, ultrathin two-dimensional (2D) sliding FEs without a phase-matching bottleneck usually exhibit pronounced second-harmonic generation (SHG) responses. Despite that the structural polarity of sliding FEs can be precisely detected via SHG characterizations, distinguishing the orientations of sliding ferroelectricity based on SHG responses has rarely been realized, as SHG intensities for upward and downward polarization states are supposed to be same. In the current work, combining computational simulations and experimental characterizations, the orientation of sliding ferroelectricity is demonstrated to be readily distinguishable via SHG responses in 2D ${\mathrm{SnP}}_2{\mathrm{S}}_6$ (${\mathrm{SnP}}_2{\mathrm{Se}}_6$), a potential sliding FE material. Specifically, owing to the unique symmetry operation within FE-${\mathrm{SnP}}_2{\mathrm{S}}_6$ (${\mathrm{SnP}}_2{\mathrm{Se}}_6$), the intersection between ${\chi }_{xxx}$ and ${\chi }_{yyy}$ SHG susceptibility coefficients with opposite signs leads to the effective rotation of SHG polar directions upon switching of sliding ferroelectricity. Moreover, the remarkable dependence of SHG polar directions on the orientation of sliding ferroelectricity is further validated by experimental characterizations performed on ${\mathrm{SnP}}_2{\mathrm{S}}_6$ crystal in a single FE domain structural form. In this work, we open an avenue for in situ detecting of the ferroelectricity orientation of 2D sliding FEs based on SHG nonlinear optical responses and demonstrate the controllable optical nonlinearity for slidetronics applications.

The equation of state (EOS) of hydrogen isotopes under extreme conditions is fundamental to planetary science and inertial confinement fusion (ICF), yet experimental constraints across broad thermodynamic regimes remain sparse. We report laser-driven shock measurements on hydrogen and deuterium statically precompressed to record pressures of 5.1 and 6.2 GPa, respectively. By coupling an integrated static-dynamic compression platform with a rigorous precompression-corrected impedance-matching framework, we extract high-precision pressure-density-temperature data up to 158.8 GPa for ${\mathrm{H}}_2$ and 281.9 GPa for ${\mathrm{D}}_2$. These measurements systematically expand the accessible phase space, exhibiting excellent agreement with a wide-range EOS model and establishing stringent benchmarks for modeling giant planetary interiors and ICF plasmas.

The description of electron-electron scattering presents challenges in the microscopic modeling of the interaction of ultrashort intense laser pulses with solids. We extend the semiclassical approach based on the Vlasov equation [M. Tani et al., Phys. Rev. B 104, 075157 (2021)] to account for dynamic electron-electron scattering by introducing the Vlasov-Uehling-Uhlenbeck (VUU) equation. We further couple the VUU equation with Maxwell's equations to describe the laser pulse propagation. We apply the present approach to simulate laser-electron interactions in bulk and thin-film aluminum, focusing on energy absorption and transport. Our calculation results reveal that electron-electron scattering affects energy absorption more significantly under $p$ polarization than under $s$ polarization, highlighting the role of the nonuniform surface potential. Our simulations also show that the energy transport extends beyond the optical penetration depth, which is consistent with observations in previous laser ablation experiments. The developed Maxwell-VUU approach is expected to advance the understanding of intense laser-material interactions not only as a cost-effective alternative to the time-dependent density functional theory (TDDFT), but also by incorporating fermionic two-body collisions whose description is limited in TDDFT.

We study prethermal time quasicrystalline (TQC) order in a quasiperiodically driven chain of noninteracting spin-1/2 particles. The drive consists of two parts, switched on and off periodically with frequency ${\omega }_d$: (i) disordered Ising interactions, with exchange couplings chosen from a symmetric interval $[-J/2,J/2]$, allowing random antiferromagnetic or ferromagnetic nearest-neighbor couplings, together with a random transverse field; and (ii) a rotating transverse magnetic field with frequency $\mathrm{\Omega }$. The ratio $\mathrm{\Omega }/{\omega }_d$ is chosen to be irrational, producing multiple incommensurate frequencies and yielding quasiperiodic dynamics beyond Floquet theory. Using exact diagonalization, we analyze the time autocorrelation function, dynamical structure factor, and entanglement entropy (EE). In the high-frequency regime, robust spectral peaks at incommensurate frequencies (not integer multiples of the fundamental drives) signal quasiperiodic time-translation symmetry breaking (QTTSB). The EE exhibits sublinear power-law growth followed by a prethermal plateau, indicating suppressed resonant heating due to an energy scale mismatch. The nonequilibrium lifetime increases rapidly with driving frequency. Unlike symmetric disorder sampling, an asymmetric distribution of the Ising exchange couplings induces collective spin rigidity, enhancing the system's resistance to heating. The TQC phase remains stable against next-nearest-neighbor (NNN) exchange perturbations and rotational imperfections, with robustness comparable to discrete time crystals (TCs) under periodic driving. Our results establish this quasiperiodically driven system as a platform for long-lived nonequilibrium temporal order, revealing the interplay of disorder, collective rigidity, and quasiperiodic driving.

A dynamical bulk-edge relation in quantum walks has been theoretically proposed and experimentally observed, in which a power-law dependence of the bulk loss probability is associated with a pronounced peak of loss probability at the edge. This behavior has been proven to arise from imaginary gap closing and the non-Hermitian skin effect in the infinite limit without boundary effects. However, in a finite-size chain, we find that boundary scattering can suppress this edge burst. Meanwhile, imaginary gap opening, together with the non-Hermitian skin effect, can also induce a large loss probability at the edge. Our results provide insights into finite-size quantum dynamics.

We present a comparative Raman scattering study of metallic rutile oxides ($\mathrm{Ru}{\mathrm{O}}_2$ and $\mathrm{Ir}{\mathrm{O}}_2$) and insulating rutiles ($\mathrm{Ti}{\mathrm{O}}_2$ and $\mathrm{Sn}{\mathrm{O}}_2$). Temperature-dependent Raman spectra reveal that metallic compounds exhibit pronounced phonon frequency hardening $[\omega \left(11K\right)-\omega \left(300K\right)=\mathrm{\Delta }\omega \approx 6-10\mathrm{c}{\mathrm{m}}^{-1}]$, whereas the insulating rutiles show only modest hardening $\mathrm{\Delta }\omega \approx 1-3\mathrm{c}{\mathrm{m}}^{-1}$. In contrast, the linewidth changes $\mathrm{\Delta }\mathrm{\Gamma }\approx 1–7\mathrm{c}{\mathrm{m}}^{-1}$ do not display a systematic metallic-insulating classification. Fits with the conventional Klemens anharmonic decay model reproduce the overall temperature trends but yield inconsistent anharmonic parameters for the metallic compounds when benchmarked against insulating rutile analogs. A modified Klemens framework, incorporating an additional $T^2$ correction to the phonon frequency arising from the electronic contribution to the phonon self-energy, quantitatively accounts for the enhanced renormalization observed in metallic systems. These results establish finite nonadiabatic electron-phonon coupling in metallic rutiles and demonstrate that phonon renormalization can be identified even in the absence of observable Fano asymmetry in the phonon line shapes.

Motivated by the objective of quantifying the energetic cost of accessing boundary phases through local control, we investigate here a simple, analytically tractable quantum impurity model. This model exhibits a rich boundary phase diagram, characterized by phases with different numbers of edge states. By considering a local quench protocol that drives the system out of equilibrium, we calculate exactly the resulting quantum work distribution across these phases. Our results show that the presence of edge states strongly alters this distribution. In particular, we analytically determine the signatures of these states in the low-, intermediate-, and high-energy sectors.

The development of two-dimensional (2D) magnetic materials provides an ideal platform for the discovery and manipulation of topological spin textures. However, most 2D materials can only support one kind of spin textures, which severely limits their diversity and potential applications. In this study, we investigate the $\mathrm{CrZn}{X}_2$ ($X=\mathrm{S}/\mathrm{Se}/\mathrm{Te}$) monolayers with ${\mathrm{D}}_{2\mathrm{d}}$ symmetry using first-principles calculations, atomistic spin simulations, and micromagnetic simulations. Our results demonstrate that domain-wall antiskyrmions can be stably hosted in $\mathrm{CrZnS}{\mathrm{e}}_2$, and under biaxial strain, they can transform to antiskyrmions. Furthermore, by tuning the in-plane magnetic field, we can induce a topological phase transition from antiskyrmions to antibimerons. We then investigate the dynamics of antiskyrmions and reveal the dependence between the antiskyrmion Hall angle and the angle of spin current injection. Under spin-orbit torque (SOT) driving, the speed of the antiskyrmion can be effectively controlled by adjusting the direction of the spin current. This design allows the antiskyrmion to move precisely along the track direction by applying an oblique spin current, thereby preventing its annihilation at the edges. This study not only uncovers diverse topological spin structures in $\mathrm{CrZnS}{\mathrm{e}}_2$ but also proposes a practical method for current-driven manipulation of antiskyrmions.