Resonant Inelastic x-ray Scattering (RIXS) is a well-established tool for probing excitations in a wide range of materials. The measured spectra strongly depend on the scattering geometry via its influence on the polarization of the incoming and outgoing light. By employing a tensor representation of the four-point response function that governs the RIXS intensity, we disentangle the experimental geometry from the intrinsic material properties. In dipole-dipole RIXS processes and low-symmetry crystals, up to 81 linearly independent fundamental spectra can be measured as a function of light polarization. However, for crystals or molecules with symmetry, the number of independent fundamental spectra that define the RIXS tensor is significantly reduced. This work presents a systematic framework for determining the number of fundamental spectra and expressing the RIXS tensor in terms of these fundamental components. Given a specific experimental geometry, the measured spectrum can be represented as a linear combination of these fundamental spectra. To validate our approach, we performed calculations for different point group symmetries, both with and without an applied magnetic field. Within the same framework, we derived expressions for powder spectra in momentum-independent processes and spectra obtained using Bragg spectrometers. This formalism provides a valuable toolkit for optimizing experiment planning, data interpretation, and RIXS simulation.

The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wave function itself remains only partially understood. In this work, we introduce a family of multipartite entanglement measures that probe chirality directly from the bulk wavefunction. Our construction involves applying different permutations between replicas of the ground-state wave function in neighboring spatial regions, creating “permutation defects” at the boundaries between these regions. We provide general arguments for the robustness of these measures and develop a field-theoretical framework to compute them systematically. While the standard topological field-theory prescription misses the chiral contribution, our method correctly identifies it as the chiral conformal field-theory partition function on high-genus Riemann surfaces. This feature is a consequence of the bulk-edge correspondence, which dictates that any regularization of the theory at the permutation defects must introduce gapless boundary modes. We numerically verify our results with both free-fermion and strongly interacting chiral topological states and find excellent agreement. Our results enable the extraction of the chiral central charge and the Hall conductance using a finite number of wave function replicas, making these quantities accessible to Monte Carlo numerical techniques and noisy intermediate-scale quantum devices.

Quantum simulations are a powerful tool for exploring strongly correlated many-body phenomena. Yet, their reach is limited by the fermion sign problem, which renders configuration weights negative, thereby compromising statistical sampling. In auxiliary-field quantum Monte Carlo calculations of the doped Hubbard model, neglecting the sign $\mathcal{S}$ of the weight leads to qualitatively wrong results—most notably, an apparent suppression rather than enhancement of $d$-wave pairing at low temperature. Here we approach the problem from a different perspective: Instead of identifying negative-weight paths, we examine the statistics of measured observables in a sign-resolved manner. By analyzing histograms of key quantities (kinetic energy, antiferromagnetic structure factor, and pair susceptibilities) for configurations with $\mathcal{S}=\pm 1$, we derive an exact relation linking the bias from ignoring the sign to the difference between sign-resolved means, $\mathrm{\Delta }\mu$, and the average sign, $\langle \mathcal{S}\rangle$. Our framework provides a more precise diagnostic of why observables such as the $d$-wave susceptibility are especially sensitive to the sign problem.

Accurate wave-function descriptions of pristine and defected solids remain challenging because of the simultaneous presence of finite-size, basis-set, and correlation errors. While embedding techniques alleviate finite-size effects and correlated wave-function approaches systematically improve correlation, basis-set incompleteness continues to limit practical accuracy. Here, we present a study of transcorrelated (TC) many-body wave-function methods on properties of solid state systems. We augment the existing xTC theory to periodic systems, and establish an unified transcorrelated embedding framework that integrates periodic TC theory with fragment-based correlated solvers. Using silicon as a test case, we validate the method against coupled-cluster, FCIQMC, and diffusion Monte Carlo benchmarks for bulk. Then, we apply transcorrelated embedding to the calculation of formation energies of two silicon self-interstitials. The TC Hamiltonian yields rapid basis convergence and quantitatively reliable defect formation energies at the triple-$\zeta$ level, substantially reducing the basis-set bottleneck for wave-function treatments of crystalline defects.

We study the van der Waals force at equilibrium between two Weyl semimetal particles. The dielectric response of the Weyl semimetal is nonreciprocal, giving rise to a repulsive force that depends on the relative alignment of the Weyl nodes of the particles. However, the aforementioned response is accompanied by a metalliclike contribution that precludes the controllability of the force sign. We show that a dielectric medium other than vacuum can yield an interparticle separation range for which the force sign can be changed by simply switching the alignment direction of the Weyl nodes of the particles. We analyze general conditions for van der Waals force repulsion between anisotropic particles and show that controlling the sign of the force requires a background medium with a large dielectric function at frequencies close to those associated with the Fermi energies of the Weyl semimetal particles. As temperature rises, the regime of force-sign controllability gradually deteriorates and eventually disappears. We discuss possible experimental implementation of our setup: background medium dispersion and force measurement. Despite current challenges in liquid materials and force detection, this should become feasible with upcoming advances. Our work might have implications on the dynamics of the motion of nanoscale devices.

In a hybrid system consisting of two quantum dots (QDs) coupled to a superconductor (SC), zero-bias peaks in the differential conductance spectrum have been reported as potential signatures of Majorana fermions (MFs). However, such signatures are typically associated with modes that appear only at specific parameter values of the QDs—so-called sweet spots—and are referred to as the poor man's Majorana (PMM). To investigate whether these signatures can be conclusively attributed to genuine MFs emerging in the practical physical parameter values, we present an alternative approach that microscopically incorporates the superconducting effects into the QDs, rather than simply attributing them to two phenomenological parameters of QDs. This forms the dressed Majorana fermions (DMFs), which can be viewed as superpositions of quasiexcitations from both the QDs and the SC. We show that DMFs can localize at one end of a one-dimensional SC and emerge in a set of the practical physical parameters, thereby enhancing the feasibility of experimental detection. Our results provide a more accurate description of the PMM in such hybrid systems and offer practical guidance for observing end-localized PMM modes in continuous one-dimensional SC.

Surface acoustic waves (SAWs) provide a versatile platform for signal processing, sensing, and emerging quantum technologies, yet their functionality is often constrained by diffraction-induced spreading. Here we introduce perfect self-similar beams (PSSBs) into acoustics and develop a theoretical and numerical framework adapted for SAWs on $\mathrm{LiNb}{\mathrm{O}}_3$. Starting from the paraxial wave equation, we derive a closed-form error-function solution for an odd-symmetric 0/π entrance and design a dislocated interdigital transducer layout to encode the required phase distribution. To bridge the gap between ideal continuous apodization and practical implementation, we further introduce a multilevel voltage driving scheme to approximate the target transverse amplitude profile with high fidelity. Three-dimensional full-wave simulations confirm the hallmark properties of SAW PSSBs, including nondiffracting propagation, self-similar scaling, a robust central null, and self-healing after partial obstruction. This work establishes both a theoretical framework and a practical strategy for shaping diffraction-resilient SAW beams, with potential applications in micro/nano manipulation, phononic information processing, and acousto-optic or quantum coupling.

We investigate the inverse Edelstein effect in a nonhomogeneous system consisting of a ferromagnetic layer coupled to a Rashba two-dimensional electron gas. Within a semiclassical Boltzmann framework, we derive analytical expressions for the charge and spin currents and analyze their dependence on key parameters such as the chemical potential and the Rashba coupling strength. We show how interfacial exchange and spin-orbit interactions jointly control the efficiency of spin-to-charge conversion, leading to distinct regimes characterized by qualitatively different transport responses. A central outcome of our work is the availability of closed-form analytical results, which provide direct physical insight and enable a transparent and quantitative benchmarking with experiments on complex oxide interfaces, such as ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$.

Topological insulators represent a class of quantum materials exhibiting a host of unique physical properties. As an important category of topological insulators, quantum spin Hall insulators show one-dimensional topological helical edge states. Here, we report the successful growth of the high-quality ultrathin ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ film on a Nb-doped ${\mathrm{SrTiO}}_3$(001) substrate by molecular beam epitaxy. With a ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ island around one quintuple layer higher than the three quintuple layer thick film, one-dimensional edge states between even and odd quintuple layers (i.e., between the island and the film) are directly observed by scanning tunneling microscopy and spectroscopy. Combined with theoretical prediction, our work provides the signature of the existence of the quantum spin Hall phase in ultrathin ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ film, and offers a platform for exploring one-dimensional helical edge states and related quantum devices.

We propose a theoretical framework to engineer hybrid-order and higher-order topological phases in three-dimensional topological insulators by coupling to $d$-wave altermagnets (AMs). The presence of only a $d_{x^2-y^2}$-type AM drives the system into a hybrid-order topological phase where both first-order and second-order topological phases coexist. This phase is characterized by spectral analysis, low-energy surface theory, and dipolar and quadrupolar winding numbers, and its signature is further confirmed by two-terminal differential conductance calculations. Incorporation of the $d_{x^2-z^2}$-type AM drives the system into two second-order topological insulator phases hosting a distinct type of hinge modes. These two variants of second-order topological phases are also topologically characterized by spectral analysis, topological invariants, low-energy surface theory, and transport calculations. Importantly, the localization and direction of propagation of these one-dimensional hinge modes are controllable by tuning the relative strengths of the altermagnetic exchange orders. We utilize this feature to propose a tunable current switching behavior mediated via the hinge modes. Our results establish an AM-based hybrid structure as a versatile platform for controllable higher-order topology and hinge-mediated device applications.

The phenomenon of Hilbert space fragmentation, whereby dynamical constraints fragment Hilbert space into many disconnected sectors, provides a simple mechanism by which thermalization can be arrested. However, little is known about how thermalization occurs in situations where the constraints are not exact. To study this, we consider a situation in which a fragmented $1d$ chain with pair-flip constraints is coupled to an ergodicity-restoring thermal bath at its boundary. We numerically observe an exponentially long thermalization time in Hamiltonian dynamics, manifested in both entanglement dynamics and the relaxation of local observables. To understand this, we study an analogous model of random unitary circuit dynamics, whose thermalization time we prove scales exponentially with system size. Slow thermalization in this model is shown to be a consequence of strong bottlenecks in configuration space, which restrict how the system can explore Hilbert space, and demonstrate another way of producing anomalously slow thermalization dynamics.

In this paper we consider quantum Hamiltonians with time-dependent interaction strengths, and following the recently formulated generalized Bethe ansatz framework [Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that constraints imposed by integrability take the same form as the renormalization group flow equations corresponding to the respective Hamiltonians with constant interaction strengths. As a concrete example, we consider the anisotropic time-dependent Kondo model characterized by the time-dependent interaction strengths $J_{\parallel }\left(t\right)$ and $J_{\perp }\left(t\right)$. We construct an exact solution to the time-dependent Schrodinger equation, and by applying appropriate boundary conditions to the fermion fields we obtain a set of matrix difference equations called the quantum Knizhnik-Zamolodchikov equations corresponding to the XXZ $R$-matrix. The consistency of these equations imposes constraints on the time-dependent interaction strengths $J_{\parallel }\left(t\right)$ and $J_{\perp }\left(t\right)$, such that the system is integrable. Remarkably, the resulting temporal trajectories of the couplings are shown to coincide exactly with the renormalization group flow trajectories of the static Kondo model, establishing a direct and universal correspondence between integrability and renormalization group flow in time-dependent quantum systems.

Defect engineering of two-dimensional materials routinely produces local magnetic moments, yet itinerant half-metallic ferromagnetism remains elusive—experiments frequently yield paramagnetic insulators. We resolve this paradox for vacancy-doped monolayer $1T\text{−}{\mathrm{TiS}}_2$ by demonstrating that the insulator-to-half-metal transition is governed by universal geometric percolation of the defect network, extending the percolation framework established for three-dimensional diluted magnetic semiconductors into the 2D vacancy-doped regime. Half-metallicity emerges via a two-step mechanism: Crystal-field symmetry breaking ($O_h\to C_{4v}$) selectively stabilizes the Ti $3d_{z^2}$ orbital, generating robust local moments ($0.94{\mu }_B$), but spin-polarized transport requires these moments to form a spanning cluster. At critical vacancy concentration $x_c\approx 12.5\%$, a percolation transition drives the majority-spin impurity band from flat, localized levels ($W<0.1\mathrm{eV}$) to a dispersive 1.5-eV wide band with 100% spin polarization and a minority-spin gap of 1.0 eV. Finite-size scaling yields a Fisher exponent $\tau =2.09\pm 0.03$, confirmed by fractal scaling of ab initio charge densities (${\tau }_{\text{eff}}^{\text{DFT}}=1.87\pm 0.26$), placing the transition in the 2D percolation universality class. The percolation mechanism is independently corroborated by a striking supercell-size effect: at identical concentration, $2\times 2$ cells yield antiferromagnetic order while $4\times 4$ cells mandate ferromagnetism, reflecting the presence or absence of a spanning cluster. We estimate a Curie temperature exceeding 300 K from the exchange coupling, and identify a geometric jamming instability at $x>20\%$ that fragments the network. These results define a narrow functional window ($11\%<x<15\%$) for half-metallic operation and establish geometric connectivity as a quantitative design principle for defect-engineered 2D spintronics.

Strongly covalent-bonded metallic compounds have emerged as promising high-temperature superconductors since the discovery of record-holding 39 K superconductivity in ${\mathrm{MgB}}_2$. Yet, recent theoretically designed lightweight high-critical temperature ($T_{\text{c}}$) covalent superconductors lack thermodynamic stability, a key prerequisite for experimental validation. Herein, we propose an effective template-guided strategy, designing nine fully $\sigma$-bonded metal boride superconductors with $T_{\text{c}}$ exceeding ${\mathrm{MgB}}_2$. Machine-learning accelerated structure searches combined with anharmonic calculations confirm $F\overline{4}3m\text{−}{\mathrm{Sr}}_2{\mathrm{B}}_5$ to be thermodynamically stable at 38–54 GPa and retain dynamic stability at ambient conditions. The calculated $T_{\mathrm{c}}$ reaches around 90 K at 40 GPa, dominated by strong coupling between the metallized $\sigma$ electronic states and $E$ phonon modes of boron atoms. Our design concept may advance the development of high-$T_{\mathrm{c}}$ lightweight covalent superconductors that can survive at room pressure.

Understanding the storage forms of manganese during Earth's evolution is essential for elucidating the origin of large-scale manganese deposits associated with the Great Oxygenation Event. Here, in addition to known manganese oxides, we identify an unconventional Mn-rich compound, ${\mathrm{Mn}}_4\mathrm{O}$, which exhibits thermodynamic stability from ambient pressure up to at least 150 GPa—the highest pressure explored. Additionally, a high-pressure polymorph of ${\mathrm{Mn}}_3{\mathrm{O}}_4$ with monoclinic $Cc$ symmetry emerges as stable above 72 GPa. Ab initio molecular dynamics simulations confirm that both phases remain in the solid state across a wide pressure-temperature range relevant to deep-mantle conditions. We propose that ${\mathrm{Mn}}_4\mathrm{O}$ may form via redox reactions between manganese and oxidized species transported by subducted hydrated lithosphere, and subsequently be brought to the surface through mantle convection, where it oxidizes into conventional manganese ores in the presence of ${\mathrm{O}}_2$. Owing to their low sound velocities, these phases could contribute to the seismic anomalies observed in ultralow velocity zones near the core-mantle boundary. These findings suggest a previously unrecognized deep-mantle reservoir for manganese and offer insights into the deep-cycle behavior of this key transition metal.

The atomic-scale structure and melting curve of liquid mercury was measured using in situ synchrotron x-ray diffraction (SXRD) at pressure and temperature ($p\text{−}T$) conditions up to 9.44(2) GPa and 651(1) K. Ab initio molecular dynamics (AIMD) simulations were employed to obtain a detailed atomistic model of the liquid structure. The results reveal a pronounced flattening, and potential maximum, in the measured melting curve between 6 and 9 GPa. The structure factors $S_{\mathrm{HgHg}}\left(Q\right)$ and pair distribution functions $g_{\mathrm{HgHg}}\left(r\right)$ calculated from the AIMD simulations are in good overall agreement with the SXRD measurements under comparable reduced densities and temperatures, indicating that the atomistic structure of liquid Hg is well captured by AIMD. With increasing pressure, the principal peak in $S_{\mathrm{HgHg}}\left(Q\right)$ shifts to higher $Q$, with the subsidiary peak at $Q=2k_{\mathrm{F}}$ experiencing a concomitant shift consistent with the increased electron density. Considering the Evans $t$-matrix formulation of the Ziman theory of liquid metals, the structural $S\left(2k_{\mathrm{F}}\right)$ term is expected to have only a weak influence on the electrical resistivity under compression. In contrast, the pressure-induced broadening and shift of the $d$-projected density of states towards the Fermi level is consistent with enhanced near-resonant $d$-electron scattering, and a corresponding increase in resistivity, analogous to the behavior of first-row transition metals. Analysis of the measured $g_{\mathrm{HgHg}}\left(r\right)$ functions, and AIMD trajectories in real space, indicates that the liquid structure experiences a progressive development towards simple hard-sphere-like behavior at increasing $p\text{−}T$ along the melting curve. However, topological cluster classification analysis shows that while the structural fingerprint of liquid Hg strongly resembles an effective hard-sphere system, even at the highest pressures investigated it contains more many-body motifs than expected for this simple model.

Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual Hamiltonians. Here we show that mobility edge positions are not independent spectral features of individual Hamiltonians, but are structurally constrained across quasiperiodic Hamiltonians related by an isospectral duality. Using a bichromatic Aubry-André model as a minimal setting, we demonstrate that this constraint is encoded in an exact identity for Lyapunov exponents derived from the Thouless formula. As a consequence, the mobility edge positions are restricted to a reduced set of energies. In the self-dual limit, these mobility edge positions coincide at a single localization-delocalization transition. This structural constraint enforces a linear critical scaling of the physical Lyapunov spectrum near the self-dual point. Numerical results confirm a critical exponent consistent with the standard AubryAndré value of $\nu =1$, while simultaneously revealing a nonuniversal energy-dependent prefactor.

We study localization driven solely by interparticle interactions in moiré lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice constants, described by a spin-dependent Fermi-Hubbard-type model with short-range interlayer interactions, where quasiperiodicity emerges only through interactions. Exact diagonalization shows that quenching hopping in one layer generates an interaction-induced mosaic potential with multiple mobility edges. When both layers are dynamical, increasing interlayer interactions drives transitions among ergodic, critical, and localized regimes, with energy-dependent coexistence in certain parameter ranges. An exact mapping to a noninteracting single-particle model on a higher-dimensional structured graph provides a unified interpretation of these results and suggests an experimentally accessible route to interaction-induced moiré physics and localization.