We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of statistical mixtures, we derive an explicit expression for the size of a characteristic symmetry sector (CSS), defined as the largest subsequence of levels exhibiting non-Poissonian correlations. The CSS dimension is shown to be the size-biased average of the underlying symmetry sectors, establishing a direct link between spectral statistics and Hilbert-space structure. We apply this framework to two paradigmatic settings: Hilbert-space fragmentation and disorder-induced many-body localization. In fragmented systems, the CSS reproduces the mixture prediction and isolates correlated subsectors even when the full spectrum appears nearly Poissonian. In the disordered Heisenberg chain, spectral decimation reveals the gradual emergence of integrability through a shrinking CSS, whose statistics exhibit signatures consistent with local integrals of motion. We introduce a characteristic symmetry entropy as a finite-size scaling observable and extract, within accessible system sizes, the crossover exponents. Our results establish spectral decimation as a controlled, unbiased, and computationally inexpensive diagnostic of hidden structure in many-body spectra, capable of distinguishing between chaotic dynamics, statistical mixtures, and emergent integrability.

We studied the electronic structure of multilayer indium films grown on Si(111) using angle-resolved photoelectron spectroscopy. Quantum well state (QWS) bands derived from In $5sp$ electrons were observed in the energy range of 0–3.4 eV, and their thickness-dependent energy shifts were well reproduced by the phase accumulation model. In addition, multiple bands with small energy spacings of $\sim 0.1\mathrm{eV}$ were observed near the Si valence-band maximum. These states originate from the coupling between the In $5sp$ states and the quantized heavy-hole (HH) states in the space-charge layer of $n$-doped Si(111). With increasing thickness, the HH-like states shifted to lower energies, while a new higher-energy state emerged when they energetically overlapped with a QWS. This repeated reorganization of the HH-like states is attributed to the thickness-dependent phase shift of the In $5sp$-derived component at the In/Si interface. Furthermore, this phase shift is found to be closely related to the preferred growth of the 9-ML and 13-ML indium films.

We develop a general theory for twisted bilayer photonic crystals that takes into account both far-field response and near-field coupling. The theory is based on the framework of a generalized Rayleigh-Schrödinger perturbation theory for non-Hermitian Hamiltonians. A universal form for interlayer coupling is derived, which relates the hopping strength to the Fourier transforms of the Wannier functions in the single layer photonic crystal. For low-energy states at the K point in hexagonal lattices, the interlayer coupling reduces to that in the Bistritzer-MacDonald model for graphene. As an example, we study a twisted bilayer photonic crystal slab with air holes arranged in a honeycomb lattice in each layer. The first-order solution of our model predicts a fourfold band splitting in the far-field spectrum compared to the single-layer case, which is confirmed by numerical simulations. Moreover, our theory reveals that for low-energy states at K points, scattering toward the $\mathrm{\Gamma }$ point via the moiré potential is suppressed. Based on our theory, we propose a wide-angle, high-$Q$ tunable flat band cavity by combining the bilayer at a large twist angle with a Brillouin-zone-folding perturbation within each layer. The cavity behaves like a collection of quasibound states in the continuum with a divergent density of states, with potential applications in nonlinear optics, lasing, and quantum optics.

Recently, proximity-induced spin-orbit coupling (SOC) has been observed in heterostructures consisting of monolayer graphene (ML-G) and transition metal dichalcogenides (TMDCs), such as ${\mathrm{WSe}}_2$. Successful tuning of SOC in graphene/${\mathrm{WSe}}_2$ heterostructures by applying mechanical pressure and electric fields was also demonstrated in previous studies. In addition, theoretical calculations predicted a strong dependence of the proximity-induced SOC on the twist angle between graphene and TMDC. Here, we put these predictions to experimental test in $\mathrm{ML}\text{−}\mathrm{G}/\mathrm{ML}\text{−}{\mathrm{WSe}}_2/\mathrm{hBN}$-heterostructures, where the twist angle is determined by aligning fractured edges, and by crystallographic etching of graphene. By performing weak anti-localization measurements, we determine the strength of the Rasbha-type SOC (${\lambda }_{\mathrm{R}}$) and the valley-Zeeman-type SOC (${\lambda }_{\mathrm{VZ}}$). Our experiments confirm a strong twist-angle dependence of the proximity-induced SOC in agreement with theoretical predictions. Finally, we demonstrate the tunability of the SOC strength via mechanical pressure, which is in agreement with earlier findings.

We investigate the mechanical and vibrational properties of three quasiplanar two-dimensional (2D) monolayers (${\mathrm{Be}}_2\mathrm{C}, {\mathrm{Be}}_5{\mathrm{C}}_2$, and ${\mathrm{B}}_4{\mathrm{C}}_3$) containing hypercoordinate carbon centers. Density functional theory was employed to determine the elastic response, Young's modulus, Poisson's ratio, and dynamical stability. ${\mathrm{B}}_4{\mathrm{C}}_3$ exhibits the highest in-plane stiffness ($\sim 249\mathrm{N}/\mathrm{m}$), nearly isotropic elasticity, and large cohesive energy, consistent with high mechanical resilience. ${\mathrm{Be}}_5{\mathrm{C}}_2$ displays strong elastic anisotropy and a negative Poisson's ratio ($\nu =-0.36$), indicative of auxetic behavior. ${\mathrm{Be}}_2\mathrm{C}$ shows intermediate stiffness and moderate flexibility. Phonon dispersions confirm that all three monolayers are dynamically stable. Electron localization function and crystal orbital Hamilton population analyses reveal extensive multicenter σ networks complemented by modest π delocalization ($\sim 10–15\%$), which facilitates uniform stress redistribution under deformation. These findings connect the topology of multicenter bonding with macroscopic elastic response, offering design guidelines for lightweight and flexible 2D materials.

Helium and methane are the important constituents of ice giants in the solar system. As such, the behavior of methane-helium mixtures at high pressure offers insights into the structure and composition of interiors of ice giants. Here, we report on the room-temperature high-pressure phase diagram of methane-helium mixtures with helium concentrations from 10% to 98% examined by Raman spectroscopy and visual observation. Several two-phase equilibria and a liquid-liquid-solid three-phase equilibrium are observed upon loading and unloading pressure. Furthermore, based on the Raman vibrational frequency and corresponding full width at half maximum (FWHM) of C-H stretching vibration mode $v_1$, we estimated helium concentrations of methane-rich fluid $\left({\mathrm{F}}_1\right)$ and helium-rich fluid $\left({\mathrm{F}}_2\right)$ in different methane-helium mixtures. In addition, Raman measurements for solid phase $\left({\mathrm{S}}_1\right)$ across all mixtures suggest helium can hardly dissolve in ${\mathrm{S}}_1$ at high pressure.

We investigate quantum inverse problems in one-dimensional (1D) electronic disordered systems strongly coupled to optical cavities. More specifically, we consider the Anderson and the Aubry–André–Harper models connected to electronic reservoirs and embedded in a single-mode optical cavity. The light–matter interaction enables photon-assisted hopping processes that significantly modify the transmittance spectrum. Within the nonequilibrium Green's function formalism, we implement an inversion-based approach capable of accurately extracting the electron–photon coupling strength directly from transmittance spectra. While cavity coupling acts as a minor perturbation within the Anderson model, yielding broad yet precise parameter estimates, its influence is markedly different in the Aubry–André–Harper model. The latter exhibits a sharp metal–insulator transition in 1D, thus resulting in more pronounced cavity-induced spectral changes. This renders even more accurate inverse solutions, offering unparalleled precision in the characterization of low-dimensional disordered systems. Altogether, our results demonstrate that the quantum inverse problem provides a robust diagnostic tool for quantum materials, particularly effective for systems exhibiting metal–insulator transitions.

In this work, we report on the thermomagnetic characterization and crystalline-electric field (CEF) energy scheme of the disordered defect-fluorite ${\mathrm{Ho}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. This structural phase is distinguished by the coexistence of magnetic frustration and extensive disorder, with ${\mathrm{Ho}}^{3+}$ and ${\mathrm{Zr}}^{4+}$ sharing randomly the same $4a$ site with even 50% occupancy, and an average 1/8 oxygen vacancy per unit cell. AC magnetic susceptibility measurements performed on powder samples down to 0.5 K revealed signs of slowing spin dynamics without glassy behavior, including a frequency dependent peak at $\sim 1\mathrm{K}$. Yet, no evidence for long-range magnetic order is found down to 200 mK in the specific heat. Inelastic neutron scattering measurements show a weak, low-lying CEF excitation around 2 meV, accompanied by a broad level centered at 60 meV. To fit our observations, we propose an approach to account for structural disorder in the crystal-field splitting of the non-Kramers ${\mathrm{Ho}}^{3+}$. Our model provides an explanation to the broadening of the high-energy, single-ion excitations and suggests that the zirconate ground-state wavefunction has zero magnetic moment. Through the breaking of local symmetry, structural disorder enables the magnetic response observed in ${\mathrm{Ho}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, allowing the mixing of low-lying states at finite temperatures. Finally, we show that this scenario is in good agreement with the bulk properties reported in this work.

Many-body interactions strongly influence the structure, stability, and dynamics of condensed-matter systems, from atomic lattices to interacting quasiparticles such as superconducting vortices. Here, we theoretically investigate pairwise and many-body interaction terms among skyrmions in helimagnets, considering both the saturated ferromagnetic and conical spin backgrounds. Using micromagnetic simulations, we calculate the exchange, Dzyaloshinskii-Moriya, and Zeeman contributions to the skyrmion-skyrmion pair potential, thereby identifying the physical origin of the attractive and repulsive regimes. For small skyrmion clusters in the conical phase, three-body interactions provide a substantial contribution to the cohesive energy, comparable in magnitude to the pairwise term, whereas four-body contributions become relevant only at low magnetic fields. As the system approaches the saturated phase, higher-order terms vanish and the interaction becomes essentially pairwise. These results demonstrate that realistic descriptions of skyrmion interactions in helimagnets, especially in the conical phase, require explicit many-body terms in order to capture the behavior of skyrmion crystals and to guide strategies for controlling skyrmion phases and dynamics.

Generating and characterizing uniform and staggered spin polarization in antiferromagnets is one of the key challenges for antiferromagnetic (AFM) spintronic technology. Here, we perform perturbative theory, group-theoretical symmetry analysis, and low-energy and ab initio simulations to propose that the magnetic precession near the equilibrium magnetic axis could generate finite uniform and staggered spin polarizations at the opposite magnetic sublattices (referring to total magnetic and Néel vector generation) in a single AFM semiconductor. This response does not require the heterojunction setup and could eliminate the lattice mismatch issues at the junction. Through scrutinizing all magnetic groups with symmetrically protected vanishing magnetic moments, and especially focusing on parity-time $\left(\mathcal{PT}\right)$ invariant groups, we identify the symmetry constraints that describe the staggered spin accumulation responses, and disclose their fieldlike and dampinglike characters. This unravels a hidden spin accumulation mode in AFM semiconductors. Furthermore, we simulate such an effect using a perturbative approach and suggest that an electric gate field and Floquet light dressing can effectively manipulate these responses.

Kagome materials are known for hosting emergent quantum phenomena driven by the interaction between different lattice, charge, and spin orders. Here, we present a detailed angle-resolved photoemission (ARPES), density functional theory (DFT), and x-ray magnetic circular dichroism (XMCD) study of the electronic and magnetic structure of $R{\mathrm{Ti}}_3{\mathrm{Bi}}_4$ $(R=\mathrm{Nd}, \mathrm{Sm}, \mathrm{Gd})$. ARPES and DFT demonstrate that the bulk electronic band structure is dominated by the hybridization of the Ti bands, and the weak electron-like pocket at $\mathrm{\Gamma }$ is identified as a surface state. The isotropic XAS profile of the $M_{4,5}$ edge of the rare earth is consistent with the presence of the $R^{3+}$ oxidation state. Using the XMCD sum rules, backed by the atomic-multiplet-theory calculations, we obtain the spin and orbital magnetic moments. The Ti $L_{2,3}$-edge XMCD reveals the presence of a small magnetic moment in ${\mathrm{GdTi}}_3{\mathrm{Bi}}_4$, presumably driven by the proximity of the Ti kagome layers to the zigzag chains of Gd, while the total magnetic moment of Gd is shared by the $f$ and $d$ electrons. Our combined XMCD, ARPES, and DFT study provides an important piece of information to understand the spin-flip transitions and anomalous Hall effect observed in the $R{\mathrm{Ti}}_3{\mathrm{Bi}}_4$ kagome metals.

We use time-resolved thermometry to monitor the decay of nonequilibrium quasiparticles in superconducting Al in the temperature range from $0.3$ to $1.2\mathrm{K}$. The quasiparticle lifetime at higher temperatures ($T>0.7\mathrm{K}$) agrees well with the calculated energy flow from electrons to phonons, but at lower temperatures it is significantly shorter than the theory predicts. We show well-defined internal equilibrium of quasiparticle system in the studied thermal transients, which implicates that quasiparticle-quasiparticle relaxation is much faster than electron-phonon interaction.

In this work we extend our study of the effect of certain crystallographic defects on the spin-1/2 Kitaev honeycomb spin liquid, focusing on its gapless phase and contrasting with the gapped phase. We identify a Stone-Wales (SW) local defect consisting of a ${90}^{\circ }$ bond rotation that preserves Kitaev bond labels for edge-sharing octahedra and thereby enables exact solvability. These SW-type defects involve odd-sided plaquettes with $\pm \pi /2$ fluxes, but can be created locally. An isolated defect hosts a time-reversal pair of ground-state flux configurations with large net chirality. Certain excitations are also chiral. The chirality manifests in Majorana local Chern marker and in scalar spin chirality, producing electronic orbital magnetization. T-matrix analysis and numerics at finite defect density $n_d$ show that defect chiralities generate a topological gap of $11n_d$ protecting a Chern number $C=\pm 1$. Emergent ferromagnetic long-range Ising interactions $r^{-\gamma }$ with $2<\gamma <3$ between defect chiralities lead to a finite-temperature $T_c$ phase transition into the chiral spin liquid. The $T_c$ is proportional to $n_d$ and diverges when $\gamma \to 2$. We also consider additional solvable impurity potentials and find that $\gamma$ can be reduced to below 2.3 and correspondingly enhance $T_c$. Our results offer applications to 2D Dirac cone systems with a finite density of fluctuating Ising magnetic impurities and to identifying spin liquids with lattice defects.

The quantum behavior of light particles in solids gives rise to phenomena that cannot be captured by a classical description. We show that muon spin spectroscopy ($\mu \mathrm{SR}$), when paired with a quantum-mechanical treatment of the implanted muon, becomes a sensitive and direct probe of nuclear quantum effects. By modeling the muon as a spatially extended quantum particle, our approach captures strong anharmonic behavior. We demonstrate this in Zn-barlowite, which serves as a nontrivial test case due to its structurally complex lattice and the presence of both fluorine and hydroxyl groups. Our results establish a route for extracting nuclear quantum signatures from $\mu \mathrm{SR}$ data and open different opportunities for studying light nuclei such as hydrogen and lithium in systems where quantum fluctuations shape structure and function.

The superconducting gap is a characteristic feature of high-$T_{\mathrm{c}}$ superconductors and provides crucial information on the pairing mechanism underlying high-temperature superconductivity. Here, we employ high-resolution resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge to investigate the superconducting gap in the overdoped cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ ($T_{\mathrm{c}}=107\mathrm{K})$. By analyzing antisymmetrized, temperature-dependent RIXS spectra over a range of in-plane momentum transfers, we observe a clear suppression of low-energy spectral weight below $T_{\mathrm{c}}$, indicative of superconducting-gap formation. This suppression is most pronounced at small momentum transfers $\left[\right|{\mathit{q}}_{\parallel }|\le 0.18$ r.l.u. (reciprocal lattice units)] and corresponds to a gap size of approximately $2{\mathrm{\Delta }}_0\sim 130$ meV. Comparison with theoretical calculations of the momentum-dependent charge susceptibility supports a $d$-wave symmetry of the superconducting gap, while an isotropic $s$-wave gap fails to reproduce key experimental features. These findings establish RIXS as a powerful, bulk-sensitive probe of superconducting-gap symmetry and highlight its utility for studying materials beyond the reach of surface-sensitive techniques such as ARPES and STM.

Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction, enables an exact functional formulation expressed solely in terms of momentum occupation numbers. Employing the constrained-search formalism and exploiting a geometric correspondence between $N$-boson configuration states and their one-particle reduced density matrices, we derive the general form of the ground-state functional. Its structure highlights the omnipresent significance of one-body $N$-representability: (i) The domain is exactly determined by the $N$-representability conditions; (ii) at its boundary, the gradient of the functional diverges repulsively, thereby generalizing the recently discovered Bose-Einstein condensate (BEC) force; and (iii) an explicit expression for this boundary force follows directly from geometric arguments. These key results are demonstrated analytically for few-site lattice systems, and we illustrate the broader significance of our functional form in defining a systematic hierarchy of functional approximations.

Spin-orbit Mott insulators with the $t_{2g}^5$ electron configuration are promising platforms for the Kitaev spin liquid, yet fine-tuning of their crystal structures is essential to suppress non-Kitaev interactions. Here, we investigate the local electronic structures of the ilmenite iridates $A{\mathrm{IrO}}_3$ ($A=\mathrm{Mg},\mathrm{Zn},\mathrm{Cd}$) and the hyperhoneycomb $\beta \text{−}{\mathrm{ZnIrO}}_3$ using Ir $L_3$-edge resonant inelastic x-ray scattering (RIXS). Multiplet analysis of the RIXS spectra reveals a systematic evolution of the crystal field and intraionic interaction parameters upon chemical substitution at the $A$ site. We observe an enhancement of the trigonal distortion with increasing $A$-site ionic radius, providing a microscopic explanation for the deviation from the ideal $J=1/2$ state and the antiferromagnetic interactions identified in ${\mathrm{CdIrO}}_3$. Furthermore, the local multiplet parameters of ilmenite ${\mathrm{ZnIrO}}_3$ and hyperhoneycomb $\beta \text{−}{\mathrm{ZnIrO}}_3$ are found to be nearly identical, demonstrating that their different magnetic ground states are primarily governed by their distinct lattice structures rather than by single-ion properties. These findings establish a solid foundation for understanding how local crystal-field distortions control the magnetic Hamiltonian in Kitaev-candidate materials.

Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal memory, spatial nonlocality, and material heterogeneity on equal footing. Classical diffusion, nonlocal transport, and hydrodynamic models emerge as controlled asymptotic limits of this kernel, providing a unified constitutive description across diffusive, quasiballistic, and hydrodynamic regimes. Interfacial heat transfer is incorporated through a spatially resolved kernel formulation, in which the conventional Kapitza resistance arises as a coarse-grained limit. The kernel admits a spatiotemporal Green–Kubo representation and can, in principle, be evaluated from atomistic simulations for bulk media, providing a direct connection between microscopic dynamics and continuum transport without empirical closure. For crystalline solids, we derive explicit kernel forms in the hydrodynamic and attenuated-streaming limits and introduce a hybrid reduction that captures the coexistence of collective and quasiballistic transport. For disordered harmonic solids, the framework recovers a spatial diffusion kernel consistent with the Allen–Feldman limit. To illustrate the theory, we construct the kernel for silicon at room temperature within the relaxation-time approximation and apply it to transient thermal-grating configurations. Spatial nonlocality associated with the phonon mean-free-path distribution is the primary source of deviation from Fourier transport under these conditions, while temporal memory mainly influences short-time dynamics. These findings identify the spatiotemporal kernel as a unifying constitutive descriptor whose coarse-grained limits recover conventional transport coefficients.