Topological invariants govern many important physical properties in condensed matter systems. In this work, we obtain the complete set of topological invariants for a family of one-dimensional quasicrystals. The first and best-studied member of the family is the Fibonacci chain, while the successive ones are known in the literature as silver, bronze, etc., and collectively as the metallic mean chains. By considering rational approximants, and by making use of the relationship between these chains and two-dimensional Quantum Hall problems, we write down a gap labeling scheme for finite systems, and extend it to the quasiperiodic limit. We show, by numerical computations on open chains, that the proposed scheme correctly yields the winding numbers of edge states in each of the gaps, in all of the quasicrystals. We observe that their relationship to the two-dimensional model leads, in the strict one-dimensional chains family, to spectra forming a simplified Hofstadter “butterfly” diagram, with the analogs of Landau levels appearing in the asymptotic limit. These topological invariants for noninteracting 1D chains can be expected to remain pertinent for superconducting systems where Majorana or Aharanov bound states occur, as shown in recent studies of interacting or Josephson coupled Fibonacci chains.

We theoretically introduce a quasi-one-dimensional magnetic heterostructure of alternating 2D topological and normal insulator strips. Such a structure can be realized by special fabrication techniques or may emerge naturally in twisted bilayers of certain transition metal dichalcogenides. Its low-energy physics is governed by a hybrid Hamiltonian intertwining the Su-Schrieffer-Heeger and Shockley models, with spin-momentum locking and local Zeeman splitting. Symmetry analysis places it in class AIII, characterized by chiral symmetry and a $\mathbb{Z}$ topological invariant. Computing the winding number from the block-off-diagonal structure of the Hamiltonian reveals topological phases characterized by invariants $\nu =0$, 1, and 2. Furthermore, a single magnetic defect acts as a sensitive local probe, whose in-gap spectrum provides a spectroscopic fingerprint to distinguish global topological phases. We show that the frequency-dependent optical absorption induced by such a defect exhibits distinct features in the topological and trivial phases, offering an independent, experimentally accessible local indicator of the global topological order. Extending the platform to a multilayer geometry uncovers a nonsymmorphic projective symmetry that gives rise to Möbius band topology.

Recent advances in on-surface chemistry, combined with scanning probe microscopy, have enabled the synthesis of correlated molecules on surfaces and the characterization of their chemical and electronic properties with unprecedented spatial resolution. Low-energy magnetic excitations of individual molecules are frequently investigated by scanning tunneling spectroscopy (STS) and often appear as symmetric step-like features in the differential conductance as a function of bias voltage. The interpretation of such steps is well established within cotunneling theory and effective model Hamiltonians (e.g., Hubbard- and spin-based models). Here, we extend the cotunneling formalism to general multireference systems. We show that multireference character, together with orbital-dependent and strongly asymmetric tip/substrate couplings, can produce pronounced asymmetric line shapes in inelastic STS. These results provide an alternative microscopic mechanism for asymmetric inelastic steps and peaks near the Fermi level frequently observed in STS experiments. In contrast to Kondo or Fano mechanisms, the asymmetry discussed here does not require a many-body resonance pinned to the Fermi level nor interference between a resonant and a non-resonant tunneling channel; it follows from the orbital composition of the neutral and virtually charged multiplets and can therefore appear at the bias of a finite-energy molecular excitation.

The Belavkin version of the quantum Cramér-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of the quantum metric. We elaborate that because the quantum metric itself is the covariance of the generators of translation in the parameter space, the quantum metric in any dimension is bounded by a product of itself and Berry curvature. The generator formalism further indicates that the bound is equivalent to a single-observable uncertainty relation for systems described by multiple observables, which in the two-observable case recovers the Robertson-Schrödinger uncertainty relation. The momentum space quantum metric and spin operators of three-dimensional (3D) topological insulators under magnetic field are used to demonstrate the validity of these bounds, and their constraints on the spread of Wannier function, absorbance in 2D, and the dielectric function in 3D will be elaborated.

In this work, we develop a new framework for computing atom-resolved contributions to optical properties based on atoms-in-molecules (AIM) schemes. The formalism is independent of the specific AIM method and is made rigorous by partitioning momentum matrix elements into atomic contributions while exactly satisfying the relevant sum rules. Zincblende GaP provides a two-atom demonstration of the atom-resolved second-harmonic-generation (SHG) analysis using five AIM partitioning methods. The two-center Ga-P channels account for $80.6\%–82.2\%$ of the SHG response, despite the pronounced partition dependence of the atomic charges. We then apply the framework to six representative ultraviolet nonlinear-optical crystals: $\beta \text{−}{\text{BaB}}_2{\text{O}}_4$ (BBO), ${\text{LiB}}_3{\text{O}}_5$ (LBO), ${\text{CsB}}_3{\text{O}}_5$ (CBO), ${\text{CsLiB}}_6{\text{O}}_{10}$ (CLBO), ${\text{KBe}}_2{\text{BO}}_3{\text{F}}_2$ (KBBF), and ${\text{LiCs}}_2{\text{PO}}_4$ (LCPO). The atom-triplet decomposition shows that two-center channels dominate the principal SHG components, while on-site terms are smaller and multicenter terms provide an important secondary contribution. Although the AIM charges, detailed local percentages, and exact pathway ranks depend on the partition, the physical interpretation remains stable across the tested AIM methods. B/O-only pathways dominate the leading responses of KBBF and LBO. Mixed pathways involving B/O or P/O atoms and cations make substantial contributions to the leading responses of BBO, CBO, CLBO, and LCPO. The decomposition framework therefore establishes a quantitative connection between local response pathways and the bulk nonlinear-optical response.

Employing a semiclassical method based on analytic continuation, we compute the electron-hole pair production rate in biased bilayer graphene subject to an in-plane electric field. This approach, originally due to Zwaan, bypasses the need for exact solutions at turning points, which are generally unavailable beyond linear or quadratic band structures. Applying this technique to biased bilayer graphene reveals nonstandard features of the asymptotic wave functions, in particular, the necessity of retaining decaying components even in classically allowed regions. By providing a fully analytic solution, this work complements and clarifies earlier results based on hybrid analytical–numerical treatments, and importantly establishes the absolute normalization of the pair production rate, and hence, of the tunneling current.

Recently, a chromium-based kagome metal $\mathrm{CsC}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_5$ has attracted significant attention due to the coexistence of density-wave-like (DW-like) orders and unconventional superconductivity; however, the nature of the DW-like orders remains elusive. Here, we perform a scanning tunneling microscopy and spectroscopy study on multiple $\mathrm{CsC}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_5$ crystals and identify a robust $4\times \sqrt{3}$ charge order (CO) on the $\mathrm{S}{\mathrm{b}}_2$-terminated surface, alongside other region-dependent charge modulations. Through comparative analysis and structural simulations, we attribute the $4\times \sqrt{3}$ CO to the coherent superposition of the underlying Sb lattice, a $2\times \sqrt{3}$ charge stripe, and additional fine-structural distortions. Our density functional theory calculations on bulk $\mathrm{CsC}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_5$ suggest that, among the considered spin density wave (SDW) configurations, a $2\times \sqrt{3}$ SDW has the lowest energy, which will induce a $2\times \sqrt{3}$ charge modulation. This provides a possible bulk-derived scenario for the $2\times \sqrt{3}$ CO component. The possible factors influencing the region-dependent charge modulations are also discussed. Our study provides a microscopic picture for the abundant COs in $\mathrm{CsC}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_5$ and highlights the propensity of magnetic kagome metals to host multiple, nearly degenerate, and competing electronic orders.

Quantum annealing with the D-Wave Advantage system in the random Ising model on a cubic lattice is simulated using a three-dimensional tensor network. The Hamiltonian is driven across a quantum phase transition from a paramagnetic phase to a spin-glass phase. The network is represented as a tensor product state, also known, particularly in two dimensions, as a projected entangled-pair state. The annealing procedure is repeated for a range of annealing times in order to test the Kibble-Zurek (KZ) power law governing the residual energy at the end of the annealing ramp. For an infinite lattice with periodic nearest-neighbor random Ising couplings, the final energy is evaluated using a deterministic method. For a finite lattice with open boundaries, we introduce a more efficient Monte Carlo sampling approach. In both cases, the residual energy as a function of annealing time approaches the KZ power law as the annealing time increases.

The imaginary-time Mpemba effect (ITME) describes a counterintuitive relaxation scenario in which a higher-energy initial state approaches the ground state faster than a lower-energy one. While most studies focus on energy relaxation, whether this anomalous hierarchy persists across other observables remains largely unexplored. Here, using exact diagonalization and Gutzwiller mean-field theory, we systematically investigate the ITME in the one- and two-dimensional extended Bose-Hubbard model—and crucially, contrast energy relaxation with that of other physical quantities, including the superfluid order parameter, local density, and trace distance. Exact diagonalization reveals that the imaginary-time Mpemba effect is controlled by the initial state's spectral projection onto low-lying eigenstates. Mean-field calculations further show that the imaginary-time Mpemba effect occurs across distinct quantum phases, including superfluid and supersolid, indicating a degree of universality. Strikingly, the relaxation of energy is not always synchronized with that of other physical quantities: Energy curves may cross even when the superfluid order parameter does not and vice versa. To further clarify the self-consistent mean-field dynamics, we analyze both the nonlinear relaxation stage and the asymptotic regime near the target fixed point. In a representative ITME case, the initially higher-energy state exhibits a stronger second-instantaneous-excited-state contribution and a larger energy-decay rate, while the late-time relaxation near the target fixed point is governed by the amplitudes of the slow relaxation modes. The results connect spectral projection, self-consistent nonlinear evolution, and observable-dependent relaxation, offering a new perspective on anomalous relaxation in strongly correlated many-body systems.

We determine the thermal melting phase diagram of the electron solid by measuring the onset density of the double-threshold voltage-current curves in the insulating state in the ultra-high-mobility two-dimensional electron system in SiGe/Si/SiGe quantum wells at different temperatures in perpendicular magnetic fields. The introduction of a magnetic field leads to a considerable increase in the onset density, which is strongest at the lowest temperatures and decreases with increasing temperature, and the melting temperature increases with magnetic field. These data are in agreement with theoretical predictions. Unexpectedly, the melting temperature as a function of electron density in a fixed magnetic field reveals a plateau, which can be interpreted in terms of resonance modes in the crystallites.

The transport properties of ${\mathrm{PdCoO}}_2$, a material with a hexagon-shaped Fermi surface, are investigated in the two contrasting crystal directions by ballistic electron deflection in a perpendicular magnetic field. By progressively reducing the device size, we systematically examine the impact of geometric confinement on the electron propagation. The measurements reveal clear orientation-dependent features. The quantitative and qualitative agreement with a theoretical model based on the Landauer-Büttiker formalism allows one to distinguish features originating from classical size effects and from the intrinsic anisotropy of the Fermi surface.

We show that in rotationally invariant spin-$3/2$ systems, the orbital Hall effect originates from interband matrix elements of the orbital magnetic moment. The resulting Hall response is governed by the quantum metric, rather than by the Berry curvature, revealing a purely geometric transport mechanism. Conventional intraband contributions associated with the orbital magnetic moment and Berry curvature are shown to vanish identically in the doubly degenerate two-band structure of the Luttinger model. These results identify the quantum metric as the key geometric quantity controlling orbital Hall transport in degenerate spin-$3/2$ systems.

A first-order structural phase transition is typically a displacive or reconstructive transformation. The latter has been considered a nondirect group–subgroup symmetry transition. However, with an alternative pathway, recent group-theoretical symmetry analysis predicts that such a reconstructive transition can be realized via a multistep displacive mode. So far, no direct observations of such a displacive transition pathway under pressure have been reported because of the lack of sufficient temporal resolution. Here, we present our experimental results on the phase transition of tin with a specially designed ultrafast time-resolved x-ray diffraction (tens of microseconds) combined with a series of rapid compressions (up to 51.5 TPa/s), revealing the missing region in both the time domain and compression-rate range between static and shock compression. The pressure-induced first-order phase transition from $\beta -\mathrm{Sn}\left(I{4}_1/amd\right)$ to γ-Sn($I4$/mmm) without direct symmetry operation shows distinct displacive characteristics in the sequential x-ray diffraction measurements, and the transition time is observed to depend on the compression rate. The deficit of summed phase fraction of β-Sn and γ-Sn from unity directly derived from diffraction peak intensities during the phase transition shows a clear compression-rate-dependent profile, which indicates the existance of an intermediate phase. Solid-state nudged elastic band calculations confirm the collective displacive paths of all atoms during the transition, and the corresponding XRD simulated patterns show results consistent with the experimental time-resolved XRD observations. This dynamic structural evolution occurs on the microsecond time scale, which is orders of magnitude shorter than conventional high-pressure XRD experiments. Our results shed new light on the dynamics of the traditionally assumed reconstructive phase transition on the microsecond time scale.

Understanding how complex entanglement structures emerge is a central problem in quantum many-body physics. Recent work by Zhang et al. [Phys. Rev. Lett. 137, 020404 (2026)] has considered structured initial states prepared by evolving a product state under a chaotic Hamiltonian for a finite time before quenching to the target Hamiltonian. In this setup, total entanglement entropy growth in many-body localized systems exhibits two distinct regimes, first increasing and then decreasing as the initial entanglement is tuned. In this work, we identify the physical origin of this behavior by analyzing the dynamics of both the Rényi entanglement entropy and the Wehrl-Rényi entropy in the random-field XXZ model, the latter of which characterizes multipartite entanglement. We show that a similar nonmonotonic dependence on the initial entanglement also appears in the net growth of the Wehrl-Rényi entropy for product states polarized along the $z$ direction. The first regime is governed by a finite local magnetization associated with local integrals of motion, while the second reflects intersite correlations. In contrast, for product states in the $x/y$ direction, the entanglement growth exhibits a monotonic decay. Our results provide a more fine-grained picture of how distinct initial-state properties shape entanglement dynamics in many-body localized systems.

Magnetoelectric multiferroics promise direct cross control between coexisting ferroelectric and ferromagnetic orders, which is of interest for applications in magnetism and spintronics. A particularly interesting type of cross control is found in spin-spiral multiferroic ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$, in which a ferroelectric multidomain distribution can be globally inverted by a single magnetic field sweep. In this work we show that this repeatable response is not obtained immediately after entering the multiferroic phase via zero-field coolling. Instead, an initial metastable multidomain state forms in which polarization, magnetization, and antiferromagnetic order do not yet minimize the trilinear magnetoelectric coupling. Using optical second-harmonic generation for ferroelectric domain imaging, we demonstrate that a single field cycle deterministically drives the system from the initial metastable state into an equilibrium domain configuration that shows repeatable domain interconversion. This initialization behavior originates from a deterministic pathway from metastable to equilibrium domain patterns, in contrast to the more common—and less reliable—stochastic domain “training” procedures that require repeated field cycles. Understanding the initial domain evolution thus enables reliable cross control in magnetoelectric devices with highly interlinked order parameters.

The interplay between spin reorientation and topological electronic structure in two-dimensional (2D) van der Waals (vdW) ferromagnets (FMs) is a core issue for understanding how magnetic anisotropy couples to nontrivial topological charge transport. Although spin reorientation transitions (SRTs) are ubiquitous in 2D metallic FMs, their role in reshaping electronic-topology–driven thermodynamic and transport properties, especially magnetotransport and thermoelectric responses, has remained largely unexplored. Here, we address this issue in ${\mathrm{Fe}}_4{\mathrm{GeTe}}_2$, a room-temperature quasi-2D vdW FM, through comprehensive temperature-dependent magnetization, specific-heat, magnetotransport, and thermoelectric measurements. Magnetization and specific-heat measurements establish a reorientation of the magnetic easy axis near $T_{\mathrm{SRT}}\sim 100\mathrm{K}$, in addition to ferromagnetic ordering at $T_C\sim 270\mathrm{K}$. Across the SRT, the Seebeck coefficient and the anisotropic magnetoresistance display pronounced anomalies, suggesting a Fermi-surface reconstruction. The magnetoresistance shows a characteristic two-step field dependence: a low-field enhancement near the SRT associated with carrier scattering from canted spins and evolving domains, followed by a higher-field negative response as spin fluctuations are progressively suppressed. The concurrent sign change of the ordinary Hall coefficient $R_0$ and the sharp anomaly in the anomalous Hall resistivity (${\rho }_{yx}^A$) across the SRT further suggest a temperature-driven modification of the underlying band topology. Furthermore, analysis of the anomalous Hall conductivity ${\sigma }_{yx}^A$ and scaling behavior of the ${\rho }_{yx}^A$ reveals that the Berry-curvature-driven anomalous Hall response below $T_{\mathrm{SRT}}$ is substantially modified above the transition. This study indicates spin reorientation as an efficient internal control parameter between distinct magnetotransport regimes in a 2D vdW FM, offering a symmetry-controlled route for engineering spin-polarized electronic states and domain-texture-driven functionalities.

Rutile ${\mathrm{RuO}}_2$ has recently attracted great interest, as its magnetic ground state remains controversial. Experimental studies have reported either nonmagnetic (NM) or altermagnetic (AM) ground states in different crystalline samples of ${\mathrm{RuO}}_2$, highlighting the need for a reasonable explanation to resolve this contradiction. In this study, density functional theory calculations are performed to reveal the correlation-sensitive and strain-dependent magnetism of bulk ${\mathrm{RuO}}_2$. On one hand, multiple AM phases with different magnitudes of the spin magnetic moment are identified for ${\mathrm{RuO}}_2$ by employing Hubbard's $U$ parameter as a perturbation probe. On the other hand, when appropriate strains that significantly change the crystal cell volume are applied, the ground state of ${\mathrm{RuO}}_2$ is suggested to undergo transitions between the NM state (with no spin splitting) and the magnetic states (with spin splitting in the band structure). These findings not only demonstrate intriguing physics in $4d$-electron-correlated ${\mathrm{RuO}}_2$, but also retain its potential for spintronic applications.