We study the interplay between nonlinearity and the non-Hermitian skin effect in the nonlinear Su-Schrieffer-Heeger model. Using a fixed-point approach, we derive stability conditions for nonlinear skin modes (skin solitons) and show that linear and nonlinear skin mode spectra coincide for semi-infinite systems. Nonlinearity typically opposes skin localization, leading to antilocalization above a critical amplitude. In finite open-boundary lattices, the model supports continuous families of edge gap solitons arising from linear zero-energy states. They become unstable in the semi-infinite limit, where strong-nonlinearity skin modes emerge. Finally, we demonstrate hysteresis in the bifurcation structure.

Controlling topological phases is a central goal in quantum materials and related fields, enabling applications such as robust transport and programmable edge states. Here, we uncover a mechanism by which local on-site impurities act as knobs to decompose global topological properties in discrete steps. In non-Hermitian lattices with spectral winding topology, we show that impurities can sequentially reduce the winding number, which is directly manifested as a stepwise decomposition of quantized plateaus in the steady-state response. Based on this principle, we further develop a scheme that sequentially induces topological edge states under impurity control, in a class of Hermitian topological systems constructed by doubling non-Hermitian ones. Such decomposition also applies to higher-order topology in two or higher dimensions. Our findings reveal a general framework to tune global topological properties with local distortions, providing a versatile route toward impurity-controlled reconfigurable topological phenomena across diverse physical platforms.

The Granovskii-Zhedanov (GZ) states are exact scar states of the spin-$S$ XYZ chain for $S\ge 1$. As a result, local quantum information encoded in a GZ state remains preserved under the unitary dynamics of the XYZ Hamiltonian; thus, these states evade thermalization and violate ergodicity despite the system being otherwise nonintegrable and chaotic. However, in realistic experimental settings, the realization of an ideal XYZ Hamiltonian is not possible, as perturbations are inevitable. These perturbations ultimately lead to the decay and thermalization of the GZ state. We study the stability and dynamics of GZ states in the presence of generic perturbations and propose physically realistic mechanisms to stabilize them. We show that the product structure of the GZ state allows its lifetime to be enhanced in the presence of an external helical magnetic field, which slows down thermalization but does not prevent it at long times. We further demonstrate that the inclusion of effective non-Hermitian spin relaxation processes can substantially stabilize the GZ states, leading to a nonequilibrium steady state with finite fidelity with GZ state. Such dissipative processes can naturally originate from mechanisms such as Purcell-enhanced spontaneous emission or spin-lattice relaxation in the presence of the helical magnetic field. Using infinite time-evolving block decimation and exact time evolution, we systematically analyze the dynamics and robustness of the GZ states in the perturbed non-Hermitian XYZ model. To connect with experimental platforms, we introduce a Hubbard model that maps onto the XYZ spin system and propose that ring-shaped optical lattices may provide a viable route for realizing and stabilizing GZ states. Finally, we present an equivalent Lindblad description of the effective non-Hermitian dynamics.

Motivated by recent theoretical predictions of a square-shaped skyrmion lattice (S-SkL) in centrosymmetric tetragonal Ce-based magnets [Y. Zha and S. Hayami, Phys. Rev. B 111, 165155 (2025)], we perform a comprehensive theoretical investigation into the role of multiorbital effects and momentum-based frustrated exchange interactions in stabilizing such topologically nontrivial magnetic textures. By employing self-consistent mean-field calculations over a broad range of model parameters, we demonstrate that the cooperative interplay among interorbital coupling, frustrated exchange interactions at higher-harmonic wave vectors, and crystal-field-induced anisotropy is crucial for the stabilization of the S-SkL. Furthermore, the competition between the easy-plane intraorbital anisotropy and the easy-axis interorbital anisotropy leads to a significant enhancement of the S-SkL stability region. We also identify a rich variety of multi-$Q$ states, including a topologically nontrivial S-SkL state with a slight breaking of fourfold rotational symmetry $\left({\mathrm{S}\text{−}\mathrm{SkL}}^{\prime }\right)$, magnetic bubble lattices (MBLs), and double-$Q$ phases with a local/net scalar chirality. Our findings elucidate the microscopic mechanism responsible for the emergence of S-SkLs in prototypical Ce-based magnets and provide a route toward realizing skyrmion lattices in a broader class of $f$-electron materials beyond conventional Gd- and Eu-based systems lacking orbital angular momentum.

Double perovskites containing $4d\text{−}4f$ interactions provide a platform to study complex magnetic phenomena in correlated systems. Here, we investigate the magnetic ground state and quasiparticle excitations of the fascinating double perovskite system ${\mathrm{Ba}}_2{\mathrm{DyRuO}}_6$ through Time of flight (TOF) neutron diffraction, inelastic neutron scattering (INS), and theoretical modeling. The compound ${\mathrm{Ba}}_2{\mathrm{DyRuO}}_6$ is reported to exhibit a single magnetic transition, in sharp contrast with most of the other rare-earth (R) members in this family, $A_2{R\mathrm{RuO}}_6$ (A = Ca, Sr, Ba), which typically show magnetic ordering of the Ru ions, followed by R-ion ordering. Our neutron-diffraction results confirm that long-range antiferromagnetic order emerges at $T_{\mathrm{N}}\approx 47\mathrm{K}$, primarily driven by $4d\text{−}4f$ ${\mathrm{Ru}}^{5+}\text{−}{\mathrm{Dy}}^{3+}$ exchange interactions, where both Dy and Ru moments contribute to the ordered state. The ordered ground state is a collinear antiferromagnet with Ising character, carrying ordered moments of ${\mu }_{\mathrm{Ru}}=1.6\left(1\right){\mu }_{\mathrm{B}}$ and ${\mu }_{\mathrm{Dy}}=5.1\left(1\right){\mu }_{\mathrm{B}}$ at 1.5 K. Low-temperature INS reveals well-defined magnon excitations below 10 meV. SpinW modeling of the INS spectra evinces complex exchange interactions and the presence of magnetic anisotropy, which governs the Ising ground state and accounts for the observed magnon spectrum. Combined INS and Raman spectroscopy reveal crystal-electric-field (CEF) excitations of ${\mathrm{Dy}}^{3+}$ at 46.5 and 71.8 meV in the paramagnetic region. The observed CEF levels are modeled through point-charge CEF calculations, consistent with the $O_h$ site symmetry of ${\mathrm{Dy}}^{3+}$. A complementary machine-learning approach is used to calculate and analyze the phonon spectrum, enabling a direct comparison with the INS data. These combined experimental and theoretical results provide a comprehensive understanding of the origin of phonon and magnon quasiparticle excitations and their influence on the crystal structure and ground-state magnetism of ${\mathrm{Ba}}_2{\mathrm{DyRuO}}_6$.

Synthetic antiferromagnetic (SAF) skyrmions are nanoscale composite textures that exhibit high-speed, Hall-free current-driven motion and have recently been shown to exhibit active-matter behavior, i.e., they can acquire self-propulsion driven by internal degrees of freedom [C. C. de Souza Silva, et al., Phys. Rev. Lett. 135, 086701 (2025)]. These remarkable properties rely on the stability of the SAF skyrmion's topological bound state, whose underlying mechanisms remain unclear. Here, using an atomistic spin model, we analyze the collapse pathways of bilayer SAF skyrmions in homochiral systems, where both ferromagnetic layers share the same Dzyaloshinskii-Moriya interaction (DMI) vectors, and in heterochiral systems, where the DMI vectors have opposite directions. We find that pair destruction occurs either by decoupling or by sequential collapse into the homogeneous antiferromagnetic state, so the activation energy is set by the smaller of these two barriers. By examining how these barriers vary with DMI strength, anisotropy, magnetic field, and interlayer exchange, we identify regimes of enhanced stability. In particular, increasing interlayer coupling strengthens homochiral skyrmions but weakens heterochiral ones, while reducing the anisotropy constant effectively stabilizes heterochiral SAF skyrmions. These results outline viable strategies to optimize SAF heterostructures for enhanced skyrmion stability in racetrack devices and emerging active skyrmionic systems.

We study bipolaron formation and bipolaronic superconductivity on a square lattice, where electrons couple to both local Holstein phonons via on-site charge density and nonlocal bond Su-Schrieffer-Heeger phonons via modulation of hopping amplitudes. Using an unbiased diagrammatic Monte Carlo method, we investigate how the interplay between these two types of electron-phonon coupling affects the bipolaron binding energy, effective mass, spatial extent (quantified by the mean-squared radius), and the superconducting transition temperature $T_c$. We find that, in some parameter space, the moderate Holstein coupling, though detrimental to $T_c$ when acting alone, can enhance superconductivity when combined with the bond SSH coupling by further compressing the bipolaron without significantly increasing its mass. Similarly, introducing bond SSH coupling into a Holstein bipolaron reduces its size while keeping the effective mass nearly unchanged, leading a higher $T_c$. These effects give rise to nonmonotonic behavior and reveal a cooperative regime in which both couplings work together to enhance superconductivity. We further examine phonon frequency asymmetry, particularly the case ${\omega }_H/t=2{\omega }_B/t$, and show that in the deep adiabatic regime, adding Holstein coupling can even raise $T_c$ when combined with bond SSH coupling. These results highlight the distinct and complementary roles of local Holstein and nonlocal bond SSH electron-phonon couplings, and suggest strategies for optimizing high-$T_c$ superconductivity in systems with multiple phonon modes.

We explore the physical consequences of enriching the U(1) order parameter of conventional superconductors to a more topologically featureful space. As an illustrative case study, we focus on fully spin-polarized triplet superconductors, which are underlied by the SO(3) $\mathbf{d}$-vector order parameter. We find that a bulk-edge correspondence links the circulation of supercurrent to the bulk magnetic skyrmions, giving rise to topological hydrodynamics of magnetic skyrmions. To probe the interplay of charge and spin dynamics, we propose a blueprint for a spin-triplet superconducting quantum interference device (SQUID), which functions without a Josephson weak link. The triplet SQUID undergoes nonsingular $4\pi$ phase slips, in which current relaxation is facilitated by spin dynamics that trace out a magnetic skyrmion texture. Inductively coupling the device to a tank circuit and probing the nonlinear supercurrent response via Oersted field measurements could provide an experimental signature of ferromagnetic spin-triplet superconductivity. Finally, we develop a general Poisson bracket formalism to describe the intertwined spin and charge dynamics such that all topological constraints are preserved, even in the presence of dissipation.

The spontaneous Hall effect, corresponding to a zero-field anomalous Hall effect (AHE), is induced by symmetry breaking associated with ferromagnetism. Studies in recent years, however, have revealed that antiferromagnetic (AFM) states characterized by magnetic point groups that allow ferromagnetism can also break the relevant symmetries and induce AHE without a large net magnetization. Here, we report that the AFM system ${\mathrm{Ce}}_2{\mathrm{PtGe}}_6$ exhibits a pronounced spontaneous Hall effect. Single-crystal neutron scattering experiments demonstrate that ${\mathrm{Ce}}_2{\mathrm{PtGe}}_6$ exhibits a collinear AFM structure with a propagation vector $\mathit{q}=0$. The small net magnetization of $\sim {10}^{-3} {\mu }_{\mathrm{B}}/\mathrm{Ce}$ indicates that the observed AHE arises from symmetry breaking inherent to its AFM structure. The anomalous Hall conductivity (AHC) reaches 300 ${\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$, which exceeds the intrinsic AHC of related compounds such as ${\mathrm{Ce}}_2{\mathrm{CuGe}}_6$ and ${\mathrm{Ce}}_2{\mathrm{PdGe}}_6$. This large AHC, most likely attributed to the large spin-orbit coupling of the Pt atoms, provides a platform for understanding the interplay between the Berry curvatures and localized $f\text{moments}$ with an AFM configuration.

This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical potential. Focusing on cylindrical geometries, we realize regions exhibiting the Laughlin-1/2 phase and its particle-hole conjugate, and confirm their topological character via the local Středa's response and Laughlin's flux insertion protocol. Our approach offers a pathway for experimentally and numerically charting entire phase diagrams within a single system, possibly eliminating the need for independent parameter scans.

Non-Hermitian (NH) Dirac semimetals describe open gain–loss systems. Yet at charge neutrality, models featuring real spectrum often look Hermitian-like, with NH effects absorbed into renormalized band parameters. Here, we show that a response-based diagnostic of effective non-Hermiticity can be formulated using minimal pseudo-Lorentz-symmetry-breaking deformations, which separate observables that remain captured by parameter redefinitions from those that exhibit irreducible NH structure. For a two-dimensional NH Dirac semimetal in the weak-NH, real-spectrum regime, we analyze Dirac-cone tilt and velocity anisotropy and compute representative probes of spectral structure, quantum geometry, optical response, and viscoelasticity at zero temperature. We find that tilt yields an NH-dependent slope of the density of states that cannot be collapsed to a single effective velocity, while velocity anisotropy can be captured by effective-velocity reparametrization. Furthermore, the quantum metric and collisionless optical conductivities provide NH-insensitive benchmarks (with the nonlinear conductivity symmetry selected), whereas the shear viscosity offers a discriminator through its tensor structure. Our results identify minimal deformations and bulk response channels that enable access to effective non-Hermiticity even when the spectrum remains real.

Intercalation of $3d$ atoms into layered transition-metal dichalcogenides (TMDs) provides an effective route to tune their magnetism and electronic structure. Using photon-energy-dependent angle-resolved photoemission spectroscopy, we show that Cr intercalation in $2H\text{−}{\mathrm{NbS}}_2$ introduces additional states at the Fermi level ($E_{\mathrm{F}}$) with appreciable $k_z$ dispersion, giving rise to a three-dimensional Fermi surface in contrast to the quasi-two-dimensional character of pristine $2H\text{−}{\mathrm{NbS}}_2$. Combined with first-principles calculations, we demonstrate that this dimensional crossover originates from interlayer hybridization between energetically aligned out-of-plane-oriented orbitals of intercalation and host-layer atoms, leading to a reconstruction of the near-$E_{\mathrm{F}}$ band manifold and enhanced interlayer hopping. Our results establish orbital hybridization as the key microscopic mechanism governing electronic dimensionality and low-energy band reconstruction in intercalated TMDs, and provide a general framework for understanding dimensional crossover in intercalated van der Waals materials.

Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems. In this paper, we establish a general framework for frustration-free fermionic systems. First, we derive a necessary and sufficient condition for a free fermion model to be frustration free. In the case of translation-invariant, noninteracting systems, we show that any band touching between the valence and conduction bands is at least quadratic. Furthermore, by extending the Gosset-Huang inequality to fermionic systems, we demonstrate that even in interacting and non-translation-invariant cases, the finite-size gap of gapless excitations scales as $O[{(logL)}^2/L^2]$, provided the ground-state correlation function exhibits a power-law decay. Our results provide a foundation for studying frustration-free fermionic systems, including flat-band ferromagnetism and $\eta$-pairing states.

Topological semimetals (TSMs), known for their topologically protected band crossings, give rise to a range of intriguing properties, including the anomalous Hall effect governed by Berry curvature in magnetic TSMs. Among these, cobalt-based magnetic TSMs, in particular, have been reported to exhibit the remarkable anomalous Hall response arising from the topologically nontrivial nodal line. In the present manuscript, we report the structural, magnetic, and magnetotransport properties of ${\mathrm{Co}}_2{\mathrm{VSn}}_{1-x}{\mathrm{Al}}_x$ ($x$ = 0, 0.25, 0.5, and 0.75), with the primary objective to experimentally understand the impact of nodal-line tuning near the Fermi level on intrinsic anomalous Hall conductivity (AHC). The tuning of nodal-line states is achieved by hole doping in ${\mathrm{Co}}_2\mathrm{VSn}$ through Al (three valence electrons) substitution at the Sn (four valence electrons) site. Our experimental results reveal that the magnitude of intrinsic AHC increases with Al doping up to $x$ = 0.5, from $\sim 148.3$ S/cm ($x$ = 0) to $\sim 203.2$ S/cm ($x$ = 0.5), showing a maximum enhancement of $\sim 40\%$ in magnitude relative to the undoped sample. Beyond this composition, a reduction in intrinsic AHC is observed. Our first-principles calculations confirm that ${\mathrm{Co}}_2\mathrm{VSn}$ hosts nodal line states, which gap out in the presence of spin-orbit coupling when the magnetization is considered along the [001] direction. Moreover, the obtained Bloch spectral function plots suggest that the nodal line gradually shifts toward the Fermi level with increasing Al substitution and nearly aligns with it for midcomposition. This results in the enhancement of total Berry curvature contribution near the Fermi level, leading to the maximum intrinsic AHC for $x$ = 0.5. Thus, the present experimental and theoretical results underscore the significance of nodal-line tuning near the Fermi level in enhancing the Berry curvature–driven AHC of the system, demonstrating a promising strategy to explore the interplay between magnetism and topological properties of the material.

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.