Non-Abelian anyonic excitations of quantum spin liquids have potential for application to topological quantum computation, but designing logical operations requires developing protocols to faithfully create, move, and read out such quasiparticles. In this paper, we test two such protocols for manipulating $Z_2$ fluxes (“visons”) of ferromagnetic and antiferromagnetic Kitaev models perturbed by a small uniform magnetic field. We show that a protocol that employs a driving magnetic field locally applied to the sites of the lattice suffers from significant unavoidable errors. These errors, accumulating over time, prevent reaching high probabilities of generating and displacing flux pairs. However, individual spin couplings can also be turned on and off, thus it is possible to create and displace fluxes with nearly $100\%$ probability. We show that braiding non-Abelian anyons can be achieved with good precision with our second protocol. We comment on the feasibility of our protocols in solid-state devices and quantum emulators.

Three-dimensional magnetic textures, such as Hopfions, torons, and skyrmion tubes, possess rich geometric and topological structure, but their detailed energetics, deformation modes, and collective behavior are yet to be fully understood. In this work, we develop an effective geometric theory for general three-dimensional textures by representing them as embedded two-dimensional orientable domain-wall membranes. Using a local ansatz for the magnetization in terms of membrane coordinates, we integrate out the internal domain-wall profile to obtain a reduced two-dimensional energy functional. This functional captures the coupling between curvature, topology, and the interplay of micromagnetic energies, and is expressed in terms of a small set of soft-mode fields: the local wall thickness and in-plane magnetization angle. Additionally, we construct a local formula for the Hopf index which sheds light on the coupling between geometry and topology for nontrivial textures. We analyze the general properties of the theory and demonstrate its utility through the example of a flat membrane hosting a vortex as well as a toroidal Hopfion, obtaining analytic solutions for the wall thickness profile, associated energetics, and a confirmation of the Hopf index formula. The framework naturally extends to more complex geometries and can accommodate additional interactions such as Dzyaloshinskii–Moriya, Zeeman, and other anisotropies, making it a versatile tool for exploring the interplay between geometry, topology, and micromagnetics in three-dimensional spin systems.

The interplay between electronic and lattice degrees of freedom is fundamental to charge density wave (CDW) formation, yet the microscopic origin often remains elusive. Here, we investigate the transient optical response of the intermetallic compound ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ using polarization-resolved ultrafast optical spectroscopy. We identify a discontinuous sign reversal in the transient reflectivity at $T_C\simeq 110\mathrm{K}$, providing unambiguous evidence for the first-order transition. The anisotropic quasiparticle relaxation establishes the three-dimensional nature of the ordered state. Below $T_C$, a single coherent 1.6 THz oscillation appears abruptly and remains confined to the CDW phase. This mode exhibits weak temperature dependence with negligible softening and is absent in Raman spectra. First-principles calculations imply that it is a precursor phonon at the CDW wave vector with strong electron-phonon coupling. Our results indicate that the CDW in ${\mathrm{BaFe}}_2{\mathrm{Al}}_9$ arises from intertwined electronic and lattice instabilities, assisted by a displacive mechanism mediated by a hidden strongly coupled phonon, distinct from conventional amplitude-mode softening scenarios.

Ultrasonic vibration has been widely applied to modify the properties of glasses, yet its influence on glass relaxation remains elusive. Here, we systematically examine the effects of ultrasonic vibrations over broad frequency and amplitude ranges on an organic molecular glass, N,N-bis(3-methylphenyl)-diphenyl-benzidine, during isothermal annealing below the glass transition temperature. Calorimetric up-scan indicates that samples annealed with ultrasound exhibit a higher probability and extent of crystallization compared to those annealed without ultrasound, while their enthalpy recovery remains unchanged. These results indicate that ultrasonic vibration facilitates local structural ordering towards crystallization, through a distinct pathway without detectably affecting the relaxation process and potential-energy evolution.

Dynamical quantum phase transitions (DQPTs) are a class of nonequilibrium phase transitions that occur in many-body quantum systems during real-time evolution, rather than through parameter tuning as in conventional phase transitions. This paper presents an exact analytical approach to studying DQPTs by combining complex dynamics with the real-space renormalization group. Renormaliztion group transformations are interpreted as iterated maps on the complex plane, establishing a connection between DQPTs and the Julia set, the boundary separating the basins of attraction of the stable fixed points. This framework is applied to a quantum quench in the one-dimensional transverse-field Ising model, where we examine the sensitivity of DQPTs to variations in boundary conditions. We show that altering the topology of the spin chain can suppress DQPTs and provide a qualitative explanation based on quantum speed limits.

We identify the mechanism of slow heterogeneous relaxation in quantum kinetically constrained models (KCMs) in which the potential energy strength is controlled by a coupling parameter. The regime of slow relaxation includes the large-coupling limit. By expanding around that limit, we reveal a nested hierarchy of states that remain frozen on time scales determined by powers of the coupling. The classification of such states, together with the evolution of their Krylov complexity, reveals that these time scales are related to the distance between the sites where facilitated dynamics is allowed by the kinetic constraint. While correlations within frozen states relax slowly and exhibit metastable plateaus that persist on time scales set by powers of the coupling parameter, the correlations in the rest of the states decay rapidly. We compute the plateau heights of correlations across all frozen states up to second-order corrections in the inverse coupling. Our results explain slow relaxation in quantum KCMs and elucidate dynamical heterogeneity by relating the relaxation times to the spatial separations between the active regions.

Validity of second-order perturbation theory (PT) is examined for magnetocrystalline anisotropy (MCA) energy in Co films with enhanced spin-orbit coupling (SOC) and Co/Pt bilayers. Comparison with accurate results obtained with the force theorem (FT) reveals significant discrepancies in the dependence of the MCA energy on the Co thickness. For systems with strong SOC, the PT fails to correctly describe the oscillations of the MCA energy, largely overestimating their amplitude and even failing (for Co/Pt bilayers) to reproduce their specific periodicity. These failures specifically concern the dominating oscillations with the two-monolayer period that arise from pairs of quantum-well (QW) minority-spin $d$ states in the Co layer, degenerate at the center of the Brillouin zone (BZ). A simplified model of such states demonstrates that the large discrepancies between PT and FT predictions arise from the breakdown of the PT in a region around the BZ center where the energy spacing between states within each pair is small compared to the SOC strength. It is also shown that the oscillation amplitude of the MCA energy calculated with the FT is limited by the finite energy spacing between consecutive QW pairs, whereas this amplitude grows quadratically with the SOC strength in the PT calculations. Furthermore, for weak and moderate SOC strengths, the accuracy of the PT diminishes with increasing the ratio of the SOC constant to temperature, which defines the broadening of energy levels. This explains why the PT overestimates the amplitude of MCA energy oscillations at low temperatures, even for the Co film with a relatively weak nominal SOC. For the Co/Pt bilayer, the strong temperature dependence of the oscillation amplitude in the PT approach leads to the MCA energies that are markedly different at low and zero temperatures, of opposite sign and several times larger in magnitude, compared to the FT results.

The dynamics of vortex states in confined geometries like thin-film disks are characterized by a subgigahertz gyration, representing the damped oscillatory motion of the vortex core about the disk center. It has recently been shown that interactions between the core and azimuthal spin waves, lying in the gigahertz range and driven by magnetic fields, can result in steady-state core gyration. The gyration in turn provides a time-periodic modulation for the spin waves, resulting in the emergence of Floquet states. Here, we present results of a theoretical and computational study in which we examine how Floquet modes sustain this core gyration. In particular, we find that multiple steady-state gyration radii are possible under certain field conditions, resulting from the nonlinear interactions between the core and Floquet modes. Different gyration radii result in distinct Floquet frequency comb spectra and allow for hysteretic effects, as reported in recent experiments.

Inspired by the recent discovery of high-temperature superconductivity in bilayer nickelates, we investigate the role of magnetism emerging from a hypothetical insulating $d^8$ parent state. We demonstrate that due to the interplay of superexchange and Hund's coupling, the system can be in a high-spin, low-spin, or spin-gapped state. The low-spin state has singlets across the bilayer in the $d_{z^2}$ orbital, with charge carriers in the $d_{x^2-y^2}$ orbital. Thus, at low energy scales, it behaves as an effective one-band system when hole doped. By contrast, the high-spin state is a more robust, spin-1 antiferromagnet. Using Hartree-Fock methods, we find that for fixed interaction strength and doping, high-spin magnetism remains more robust than the low-spin counterpart. Whether this implies that the high-spin state provides a stronger pairing glue or more strongly competes with superconductivity remains an open question. Our analysis, therefore, underscores the importance of identifying the spin state for understanding superconductivity in nickelates.

The ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ compound was investigated using dynamic magnetic measurements, microscopic ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy, complemented by density functional theory (DFT) and Monte Carlo simulations. A reliable fitting scheme was developed for its Mössbauer spectra, yielding a complete set of hyperfine parameters from 5 K to above the Curie temperature. The opposite signs of the quadrupole splitting for the FeI and FeII sites indicate that the interactions at the FeI site are predominantly out-of-plane, in contrast to the primarily in-plane interactions at the FeII site. Furthermore, the temperature dependence of the hyperfine field shows that the magnetism of ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ aligns more closely with the three-dimensional Heisenberg model. The Mössbauer spectra also reveal that intrinsic defects enhance spin fluctuations, as evidenced by the presence of a persistent paramagnetic component down to 5 K and significantly broadened linewidths. To understand the origin of these defects, we performed systematic DFT and Monte Carlo simulations. Our theoretical results demonstrate that such defects suppress the ferromagnetic transition temperature and suggest that the observed spin fluctuations are likely linked to FeII vacancies and/or FeII-Ga antisite defects.

A topological pump on an $N\text{−}\mathrm{leg}$ spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of $2N\text{−}\mathrm{site}$ staircase clusters. We define a pump path in parameter space that connects two distinct symmetry-protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump, the bulk Chern number is given by the number of critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated in association with deformation of the pump path. We find that there are $N$ critical points enclosed by the pump path for the $N\text{−}\mathrm{leg}$ ladder. The ground-state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states at the diagonal boundary and numerically demonstrate the bulk-edge correspondence for $N=2,3$ cases.

The magnetism of two-dimensional van der Waals materials has attracted significant attention due to its potential for novel spintronic applications. Strain engineering has emerged as a powerful tool for manipulating the magnetic properties of these materials. Based on density functional theory, the regulation effect of uniaxial strain on the magnetic coupling of the CrSeTe monolayer is systematically studied. We calculate the magnetic exchange constants using the first-principles linear-response method and find that the magnetic structure is dominated by $J_{1a}$ and $J_{1ab}$. The results show that the tensile strain along the $a$ axis significantly enhances $J_{1a}$, while the tensile strain along the $a$ axis or $b$ axis strengthens $J_{1ab}$. However, based on the same lattice constants as the experiment, our preliminary phase diagram predictions indicate that the magnetic ground state is ferromagnetic. It is inconsistent with the experimentally observed zigzag antiferromagnetic sequence. Therefore, the structure of the CrSeTe monolayer has been optimized based on various antiferromagnetic sequences, and the magnetic phase diagram has been reconstructed. The optimized results are in good agreement with the experimental observations, indicating that structural optimization plays a key role in understanding the magnetic properties of the CrSeTe monolayer. This study provides a theoretical foundation for strain-regulated magnetism in two-dimensional van der Waals materials, paving the way for future experimental research and device design.

We present a comprehensive investigation of the physical properties of a candidate nodal-line semimetal GdRhPb single crystals, through magnetization, heat capacity, and magnetotransport measurements. Temperature-dependent magnetization $\left[\chi \right(T\left)\right]$ along different crystallographic directions confirm that Gd ions are in the trivalent state and exhibit antiferromagnetic (AFM) ordering below $T_{N1}=17.6 \mathrm{K}$, followed by a second magnetic transition at $T_{N2}=15.3 K$. Electrical resistivity measurement exhibits metallic behavior, followed by a sharp increase at just below $T_{N1}$, indicative of AFM superzone gap formation. These AFM phase transitions are further corroborated by the temperature-dependent heat capacity. Within the AFM state, isothermal magnetization $\left[M\right(H\left)\right]$ data reveal multiple field-induced metamagnetic (MM) transitions. Moreover, transverse and longitudinal magnetoresistance data show a sharp drop at critical fields, aligning with the MM transitions observed in $M\left(H\right)$ data. Hall resistivity analysis in the paramagnetic region indicates a crossover from single carrier-dominated electrical transport to contributions from multiple carrier types. Interestingly, a distinct humplike anomaly in the Hall resistivity below $T_{N1}$, not scaling with $M\left(H\right)$, suggests the presence of the topological Hall contribution. Additionally, the constructed $H-T$ phase diagram for $H\perp c$ reveals at least four distinct magnetic phases, highlighting the compound's complex low-temperature magnetic behavior. Furthermore, first-principles calculations reveal that GdRhPb is a topologically nontrivial nodal-line semimetal, characterized by drumhead surface states and a nonzero Berry phase.

Mott insulators, in which strong Coulomb interactions fully localize electrons on single atomic sites, play host to an incredibly rich and exciting array of strongly correlated physics. One can naturally extend this concept to cluster Mott insulators, wherein electrons localize not on single atoms but across clusters of atoms, forming “molecules in solids.” The resulting localized degrees of freedom incorporate the full spectrum of electronic degrees of freedom, spin, orbital, and charge. These serve as the building blocks for cluster Mott insulators, and understanding them is an important first step toward understanding the many-body physics that emerges in candidate cluster Mott insulator materials. Here, we focus on elementary building blocks, neglecting some of the complexity present in real materials that can often obfuscate the underlying principles at play. Through an extensive set of exact theoretical calculations on clusters of varying geometry, number of orbitals, and number of electrons, we uncover some of the basic organizing principles of cluster Mott degrees of freedom, particularly when interactions dominate and negate a simple single-particle picture. These include, for example, the identification of an additional “cluster Hund's rule,” of cluster ground states that are best understood from a purely interacting perspective, and of several localized degrees of freedom which are protected by an unusual combination of discrete spatial or orbital symmetries. Finally, we discuss the impact of adding additional terms, relevant to material candidates, on the phase diagrams presented throughout, as well as the potential next steps in the journey to building a more complete picture of cluster Mott insulators.

The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying distance, in the Hubbard model at weak coupling. This allows us to investigate the spatial structure of entanglement in dependence of interaction strength, electron filling, and temperature. We compare results from different entanglement measures, and benchmark against quantum Monte Carlo.

We extend our theoretical description of optical excitations in binary plasmonic supercrystals made of two types of metal nanoparticles to three common cubic structures: sodium chloride (NaCl), zinc blende (ZnS), and auricupride (${\mathrm{Cu}}_3\mathrm{Au}$). Our microscopic model of plasmon polaritons in supercrystals incorporates dipole and quadrupole nanoparticle excitations, their interactions, and their coupling with photons. We calculate the plasmon-polariton dispersion for the three cubic structures starting from the dipole and quadrupole energies obtained in the quasistatic approximation. The bands depend on the properties of the nanoparticles as well as the symmetry and the lattice parameters of the supercrystals. To gain further insight into the coupling of different excitations and develop a set of symmetry selection rules for each structure, we complement our calculations with an extensive group theory analysis. Comparing the results across various structures makes our symmetry analysis more general, enabling us to observe selection rules that apply to multiple structures.

Recently, there has been renewed interest in coupling of spin waves (magnons) and collective charge oscillations (plasmons), especially in two-dimensional systems. Several mechanisms of the magnon-plasmon hybridization in ferromagnetic and antiferromagnetic systems have been proposed. Here, we consider another mechanism of magnon-plasmon hybridization, which is based on the linear magnetoelectric interaction. As a specific system, we consider a monolayer of vanadium-based diselenide with perpendicular easy-axis magnetic anisotropy and Dzialoshinskii-Moriya interaction. The derived parameter of magnon-plasmon coupling is proportional to the magnetoelectric constant. Assuming for this constant an adequate experimental value, we calculate dispersion relations of the hybridized magnon-plasmon modes. Moreover, we also show that an external electric field normal to the layer (due to a gate voltage) can be used as a tool to tune the magnon modes and this way also hybridized magnon-plasmon coupling. A specific case of magnon-plasmon coupling based on tuning Dzialoshinskii-Moriya interaction is also considered.

In this paper, we develop a novel theory that generalizes the concept of anyon statistics to Abelian topological excitations of any dimension. We axiomatize excitations as a selected collection of states and operators satisfying the configuration axiom and the locality axiom, purely based on many-body quantum mechanics. Upon these axioms, we define a rigorous and self-contained theory of statistics using only basic algebra that can be implemented on a computer. While our theory is developed independently, the results align with existing physical theories.

We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half filling below a transition temperature $T^{*}$. Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a nonlinear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility $S(\mathbf{q},\omega )$ has a spin gap, the static uniform spin susceptibility ${\kappa }_s$ decreases strongly with temperature below $T^{*}$, and the NMR relaxation rate $T_1^{-1}$ vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, $S(\mathbf{q},\omega )$ exhibits nematicity below a transition temperature $T_{\mathrm{nem}}<T^{*}$, and at larger hole doping in the entire pseudogap regime below $T^{*}$.