We develop a general framework based on the sign patterns of Lyapunov exponents for engineering and characterizing counterintuitive localization properties in one-dimensional non-Hermitian quasiperiodic lattices. On the one hand, for the Anderson localized states in the bulk under the periodic boundary condition, we find that their localization features can be boundary sensitive, becoming boundary-localized skin modes under the open boundary condition. On the other hand, for nonlocalized states, the well-known extended-localized duality relation can break down, as their counterparts in the dual model can also be nonlocal. We discuss how these remarkable phenomena can be understood from the perspective of Lyapunov exponents, highlighting the interplay of non-Hermiticiy and quasiperiodicity.

van der Waals antiferromagnets provide a route to thickness-controlled magnetic order, but few combine high-temperature Ising order with conducting, correlated, and topological electronic structure. Here we show that UOTe realizes this combination. Magnetic susceptibility reveals a strongly anisotropic paramagnetic response, while neutron diffraction establishes $c$-axis antiferromagnetic order below $T_{\mathrm{N}}\approx 150\mathrm{K}$ with an order-parameter exponent $\beta =0.14$, close to the two-dimensional Ising value. Torque magnetometry further shows that the ordered state remains well described by a uniaxial antiferromagnet below the high-field metamagnetic transition. Pulsed-field magnetization up to $73\mathrm{T}$ shows that the ordered state survives to very large fields applied along the $c$ axis before entering a broad metamagnetic regime that begins near $50\mathrm{T}$ and remains unsaturated at the highest measured field. Angle-dependent proximity detector oscillator measurements show that the metamagnetic instability is set by the field component along the ordered moment direction, providing direct evidence for Ising-like field rigidity. UOTe therefore establishes a field-rigid Ising antiferromagnet with giant metamagnetic transition fields in a compensated van der Waals metal, where high-temperature $c$-axis order, quasi-two-dimensional magnetic criticality, Kondo-associated uranium $5f$ hybridization, metallic transport, and symmetry-enabled topology coexist in a single material.

Body-centered-cubic $\mathrm{Ca}{\mathrm{H}}_6$ has attracted considerable attention due to its unique hydrogen clathrate structure and high-$T_{\mathrm{c}}$ superconductivity ($T_{\mathrm{c}}=215\mathrm{K}$ at 172 GPa). Although hydrogen vacancy in this hydride has been reported experimentally, its effects on structural and superconducting properties remain unclear. By comparing with the experimental equation of state, our path-integral molecular dynamics simulations reveal that pressure reduction induces hydrogen depletion from interstitial sites of the Ca sublattice, resulting in the formation of a nonstoichiometric $\mathrm{Ca}{\mathrm{H}}_{6-\delta }$ phase $\left(\delta \le 0.45\right)$ below 165 GPa. The increase in hydrogen vacancies induces thermoelastic instability below 125 GPa (at 300 K) through shear-modulus softening, while concurrently suppressing superconductivity via electronic-state modulation, with the $T_{\mathrm{c}}$ decreasing at a rate of $2.3\mathrm{K}/\mathrm{GPa}$. Both results align with experimental observations. Moreover, we predict that hydrogen vacancies facilitate hydrogen diffusion in the superconducting $\mathrm{Ca}{\mathrm{H}}_{6-\delta }$ phase between 145 and 160 GPa, with the diffusivity reaching or exceeding ${10}^{-8}\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$. The findings emphasize the key role of hydrogen vacancy in understanding the high-pressure evolution behavior of high-$T_{\mathrm{c}}$ hydrides.

Discrete time crystals (DTCs) have emerged as a novel nonequilibrium phenomenon, exhibiting spontaneous symmetry breaking of discrete time translation symmetry, and holding promise for applications ranging from enhancing quantum sensing to protecting quantum entanglement. Nevertheless, analytical quantification for disordered DTCs remains challenging, leaving uncertainties about their behaviors in large scale systems amid current debates on the stability of (Floquet-)many-body localization. In this work, we introduce an analytical framework to calculate the values of key observables in a strongly disordered DTC without fitting parameter. The perturbatively obtained closed-form formulas show quantitative agreement with numerical simulations for inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as $O\left(\lambda \right)$, in contrast to nonresonant situations with suppressed deviation $O\left({\lambda }^2\right)$. Our newly developed scheme adopts resolvent perturbation formalism, which can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order $O\left({\lambda }^{(L/n_{\text{op}})-1}\right)$, where perturbations of strength $\lambda$ involve at most $n_{\text{op}}$-spin terms. Such spectral pairing deviations quantify the DTC lifetime as ${\tau }_{*}\sim {(1/\lambda )}^{L/n_{\text{op}}}$. We further show that the analytical framework applies to generic DTC models with dominant Ising interaction and a given number of qubits, offering a unified scheme to quantify physical observables for systems beyond numerically accessible sizes, with or without disorders.

Two-dimensional (2D) altermagnets (AMs), characterized by distinctive spin splitting and robustness against external fields, have emerged as promising candidates for spintronic device applications. Exploring multipiezo effects in 2D AMs through precise and energy-efficient modulation strategies has become crucial for realizing their multifunctional applications. In this work, we demonstrate that the $\mathrm{F}{\mathrm{e}}_2\mathrm{Mo}{\mathrm{S}}_2\mathrm{S}{\mathrm{e}}_2$ monolayer is a 2D AM with a pronounced spin splitting of 0.45 eV for valence bands. The $\mathrm{F}{\mathrm{e}}_2\mathrm{Mo}{\mathrm{S}}_2\mathrm{S}{\mathrm{e}}_2$ monolayer exhibits valley degeneracy at the ${\mathrm{X}/\mathrm{X}}^{\prime }$ valleys, which is protected by $\left[C_2\parallel C_{4z}\right]$ and $\left[C_2\parallel M_{xy}\right]$ symmetries. Uniaxial strain as an energy-efficient modulation strategy breaks the balance of these symmetries. This imbalance induces piezomagnetic and piezovalley effects in $\mathrm{F}{\mathrm{e}}_2\mathrm{Mo}{\mathrm{S}}_2\mathrm{S}{\mathrm{e}}_2$ monolayer, accompanied by the emergence of an anomalous valley Hall effect. Furthermore, $\mathrm{F}{\mathrm{e}}_2\mathrm{Mo}{\mathrm{S}}_2\mathrm{S}{\mathrm{e}}_2$ monolayer possesses a Janus structure, which enables significant in-plane and out-of-plane piezoelectric effects under uniaxial strain. The multipiezo effects make the Janus $\mathrm{F}{\mathrm{e}}_2\mathrm{Mo}{\mathrm{S}}_2\mathrm{S}{\mathrm{e}}_2$ monolayer a promising platform for the development of multifunctional spintronic devices.

Topological phases in metamaterials are often inferred from localized edge states or from real-space wave-function measurements. Yet the topology is fundamentally encoded in the bulk eigenvectors and often manifests as a bulk band inversion. Here we directly access this band inversion in an exciton-polariton Su-Schrieffer-Heeger (SSH) chain using far-field spectroscopy with tuneable sublattice interference. The SSH chain provides an excellent benchmark model for establishing this measurement principle in an exciton-polariton platform. We show that in the SSH model, the band inversion is characterized by a sign change of the sublattice symmetry $\langle {\sigma }_{\mathrm{x}}\rangle$ between the Brillouin-zone center and boundary. A transverse sublattice displacement maps the relative phase between sublattice wave functions onto a controllable far-field interference phase $\mathrm{\Delta }\theta$. Taking the difference of spectra at $\mathrm{\Delta }\theta =0$ and $\mathrm{\Delta }\theta =\pi$ yields a quantity proportional to $\langle {\sigma }_{\mathrm{x}}\rangle$, directly revealing the band inversion in the topological configuration. The tunable phase $\mathrm{\Delta }\theta$ further lets us reconstruct the effective $2\times 2$ Bloch Hamiltonian and its winding number, unequivocally linking the measured band inversion to the topological invariant. More generally, spectroscopy with a controllable sublattice phase allows for the measurement of bulk eigenvectors, granting access to band inversions for higher-dimensional systems.

We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle Green's function and analyze its dynamics across a broad range of interaction strengths. To complement the time-domain approach, we develop a high-resolution Chebyshev expansion method within the density matrix formalism, enabling direct access to spectral functions in the frequency domain. As interactions are introduced, a transition in the spectral function from a sharp, free-particle dispersion to a broadened two-band structure associated with hole and electron excitations is observed, and electron propagators are found to display a diffusive falloff. At infinite interaction strength ($U=\infty$), we exploit a determinant representation of the Green's function to access both real-time and spectral properties. In this regime, spectral functions retain a blurred, cosinelike momentum dispersion in frequency space indicating almost coherent propagation, while the dynamics display nontrivial light-cone spreading with an anomalous exponent $\alpha \approx 0.78$. Our results demonstrate that strong correlations and nontrivial quantum coherence can persist even at infinite temperature and infinite interaction strength.

The hybrid skin-topological effect (HSTE) arises from the interplay between the non-Hermitian skin effect and topologically protected edge states. Here, we investigate the HSTE associated with antichiral edge states. As a minimal model, we study a modified Haldane nanoribbon in which gain and loss are applied exclusively at the zigzag edges. We show that in antichiral systems, the HSTE originates from the interplay between edge modes and counterpropagating bulk modes, a mechanism distinct from that in conventional chiral systems. Remarkably, in sufficiently narrow ribbons, applying gain or loss to only one edge can induce a skin effect in states localized at the opposite edge. We refer to this phenomenon as a nonlocal antichiral skin effect. We further show that, in narrow systems, edge-localized dissipation can induce bulk skin modes when parity-time ($\mathcal{PT}$) symmetry is broken, while the bulk non-Hermitian skin effect is forbidden in the $\mathcal{PT}$-symmetric regime. These results imply that edge-localized gain and loss can control both the emergence and the localization direction of the bulk skin modes. Our findings establish a symmetry-based mechanism for controlling non-Hermitian skin effects via edge dissipation in antichiral systems.

We study the robustness of the Floquet quantum Ising model against integrability-breaking perturbations, focusing on the phase hosting both Majorana zero and $\pi$ modes. A recent work [H.-C. Yeh, A. Rosch, and A. Mitra, Phys. Rev. B 110, 075117 (2024)] observed that the Floquet product mode, a composite edge mode constructed from both Majorana operators, is considerably more robust than the individual Majorana edge modes. We analyze these strong modes from the point of view of the eigenphase order present in finite chains with open boundary conditions. As a result of the Majorana modes, all Floquet eigenstates come in quadruplets in the integrable limit. We show that the robustness of the various modes as well as the behavior of the boundary spin correlation functions can be understood in terms of the spectral statistics of these quadruplets in the presence of integrability-breaking perturbations.

The electronic, magnetic, valley, and magneto-optical properties of an intrinsic MnBi monolayer in the hexagonal phase are investigated using first-principles calculations including on-site Coulomb interactions and spin-orbit coupling. The monolayer exhibits a ferromagnetic ground state with pronounced magnetic anisotropy, which significantly modifies the low-energy electronic structure and induces magnetization-direction-dependent band gap openings. The Berry curvature and anomalous Hall conductivity are highly sensitive to the orientation of the magnetization. A sizable valley splitting emerges for out-of-plane magnetization, while it is nearly quenched for in-plane alignment, demonstrating a strong coupling between magnetic anisotropy and valley physics. Furthermore, charge doping, external electric fields, and mechanical strain provide efficient routes to tune the magnetization orientation and Curie temperature while preserving magnetic order. These results highlight the MnBi monolayer as a promising platform for two-dimensional spintronics, valleytronics, and magneto-optical applications.

We study the effects of cavity-mediated interactions on the symmetries and topological properties of a Su-Schrieffer-Heeger chain coupled to a single-mode photonic cavity. Considering an off-resonant regime we use the high-frequency expansion in order to obtain an effective fermionic Hamiltonian with cavity-mediated interactions. We characterize the effects of the cavity on topology in a finite-size chain by studying three different fermionic many-body topological markers using exact diagonalization: correlation functions between edges in a chain with open boundary conditions, and a winding number based on the single-particle Green's function and bulk electric polarization via the many-body formula by Resta for a chain with periodic boundary conditions. Importantly, we show that chiral symmetry is not broken by the cavity in the many-body ground state in the high-frequency limit. Our work highlights the importance of the cavity-mediated many-body interactions in understanding the symmetry and topology of the system.

We investigate bias-driven nonequilibrium quantum phase transitions in a paradigmatic quantum transport setup: an interacting quantum dot coupled to noninteracting metallic leads. Using the random phase approximation, which is exact in the limit of a large number of dot levels, we map out the zero-temperature nonequilibrium phase diagram as a function of interaction strength and applied bias. We focus our analysis on the behavior of the charge susceptibility and the current noise in the vicinity of the transition. Remarkably, despite the intrinsically nonequilibrium nature of the steady state, critical charge fluctuations admit an effective-temperature description, $T_{\mathrm{eff}}(T,V)$, that collapses the steady-state behavior onto its equilibrium form. In sharp contrast, current fluctuations exhibit genuinely nonequilibrium features: the fluctuation-dissipation ratio becomes negative in the ordered phase, corresponding to a negative effective temperature for the current degrees of freedom. These results establish current noise as a sensitive probe of critical fluctuations at nonequilibrium quantum phase transitions and open directions for exploring voltage-driven critical phenomena in quantum transport systems.

Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analog to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain underexplored. Here, we study what happens to the uniform electron gas when a space-time periodic potential of arbitrary strength is applied, which leads to band splitting. The case of a potential traveling at constant speed is special, since the problem can be made time independent by transforming to a comoving frame. We perform linear-response theory, in the sense that we apply an additional perturbatively small but nonperiodic probing field, for which we illustrate the analogy of Fermi's golden rule and the photoemission spectrum of a many-electron system. As in the equilibrium case, the latter is related to the spectral function which is positive definite. We also analyze the parameter dependence of the controllable photoemission spectra by virtue of Floquet-Bloch engineering.

We study the dc conductivity of a two-dimensional Rashba system with an in-plane Zeeman field and delta-correlated scalar disorder. We show that, although the field deforms the two helicity Fermi contours and rotates the spin texture, it does not produce anisotropic magnetoresistance in the leading quasiclassical conductivity. The result follows from a geometric identity for the total area occupied by the two helicity sheets. A density Ward identity fixes the spin-vector part of the Born self-energy to the derivative of the total particle density with respect to the field. This derivative vanishes, because the total area enclosed by the two Rashba-Zeeman sheets is independent of the in-plane field. The Born self-energy is therefore scalar and field independent, and the quasiparticle lifetime stays isotropic. The same occupied-area identity controls transport: The leading impurity ladder reduces the current vertex to the parabolic velocity, and the diagonal intraband Kubo conductivity collapses onto the two-sheet occupied area and is field independent as well. Thus, pointlike nonmagnetic impurities produce neither angular anisotropy nor field-magnitude dependence in the leading diagonal two-sheet quasiclassical conductivity. Any residual AMR from delta-correlated disorder must originate from corrections outside this sector.

We explore theoretically the optical response of two-dimensional (2D) materials patterned at the nanoscale into either arrays of ribbons along a planar surface or spherical particles. Fourier-Floquet decomposition of the electromagnetic fields is used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles are treated with Mie theory, with the boundary conditions modified to accommodate a surface conductivity at the interface. We consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide ${\mathrm{WS}}_2$ in the visible. Unlike what is expected from graphene, where plasmons have proven very sensitive to geometry, the excitonic response of nanoribbon arrays is found to show weak tunability with the array parameters. To enhance tunability with the geometry of the system, or via hybridization with the substrate, nanospheres with a 2D semiconductor coating are demonstrated to provide a superior platform. Overall, we find that the localized nature of excitons in 2D semiconductors largely limits tunability with geometry, but their hybridization with other optical modes in the nanopatterning setup still holds promise for controllable light-matter interactions.

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using x-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross section, as a function of the momentum transfer and the scattering angle. Experimental verification using x rays and binary alloys appears well within the existing techniques, while feasibility for neutron scattering requires further study. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

We explore nonequilibrium topological responses of symmetry-protected topological (SPT) states in open quantum systems subject to decoherence. For SPT wave functions protected by a product symmetry $G\times S$, where $G$ defects are decorated with $S$ charge, we show that full dephasing of the $S$ charge density induces spontaneous strong-to-weak symmetry breaking (SWSSB) of $G$ in the resulting mixed-state ensemble. We extend this mechanism to SPT phases protected by higher-form and spatially modulated symmetries, and further to gapless SPT states, demonstrating that dephasing-induced SWSSB persists well beyond conventional gapped zero-form settings. Our results provide a qualitative, channel-defined fingerprint of SPT order that is intrinsic to open-system dynamics and goes beyond equilibrium linear response.

Two-dimensional (2D) altermagnets have been attracting enormous research interest; however, the general guidance of global symmetry breaking poses a significant challenge of rather limited material candidates. Here, we propose a simple and widely applicable design strategy for generating both hidden and visible 2D altermagnetism in van der Waals antiferromagnetic multilayers. Based on conventional antiferromagnetic monolayers with spacetime-inversion symmetry, different types of altermagnetism can be realized, depending on interlayer magnetic interaction and local symmetry breaking. Notably, the approach has the advantage that it does not require a specific twisting/stacking order or global inversion symmetry breaking. Using a symmetry-guided framework and high-throughput computational screening, we identify diverse hidden and visible altermagnetic candidates. Beyond bilayer thicknesses, this unconventional layer-dependent nonrelativistic spin splitting mechanism exhibits a distinct odd-even effect, differing from that in conventional A-type antiferromagnets. Leveraging hidden altermagnetic order, we propose a universal multiferroic scheme for ferroelectric reversal of spin polarization. Our study greatly expands the family of 2D altermagnetic materials, circumvents stringent constraints associated with previous methods, and opens new pathways toward altermagnetic spintronics.