The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method to Hamiltonian deformations, which provides a systematic way to construct solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace remains unchanged, and time evolution takes place in a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.

The entanglement spectrum (ES) is a powerful tool for probing topological phases. While its behavior in gapped systems is well understood, its properties in gapless regimes remain unclear. In this work, we employ a quantum Monte Carlo method to study the ES of a two-dimensional square-octagon lattice Heisenberg model at quantum criticality and in the Néel phase. We find that the ES exhibits an M-shape magnon mode with a distinct sublinear dispersion, deviating from the conventional linear magnon. This behavior, similar to that of a one-dimensional long-range Heisenberg chain, reveals the emergence of relevant long-range interactions in the entanglement Hamiltonian. We demonstrate that the mechanism underlying short- and long-range interactions in the entanglement Hamiltonian can be interpreted as the confinement/deconfinement of worldlines in the path integral formulation. Our results reveal that gapless modes can fundamentally change the entanglement Hamiltonian and its spectrum, thereby offering insight into this general phenomenon.

Driven by the need to understand and determine the presence of nontrivial superconductivity in real candidate materials, we present a generalized set of self-consistent Gor'kov-Hedin-Baym equations with spin-dependent electron-electron and electron-phonon interactions. This extends Hedin's original equations to treat quantum many-body systems where electronic and lattice correlations along with relativistic effects coexist on the same footing with superconductivity. The leading order self-energies yields a generalization of the Migdal-Eliashberg theory and by iterating this set of equations generalized ladder vertex corrections naturally emerge.

Odd-parity magnetism constitutes an intriguing phase of matter which breaks inversion symmetry while preserving time-reversal symmetry. Here we demonstrate that the Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state by combining low-energy modeling with density functional theory. In the absence of spin-orbit coupling, the electronic spins are polarized along the $k_z$ direction and the splitting of the up and down states exhibits an $h$-wave form factor. The magnitude of the splitting depends sensitively on specific parameters of the low-energy model, including specific out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. Interestingly, despite this state breaking inversion symmetry and exhibiting a finite out-of-plane Berry curvature and nonlinear anomalous Hall effect, the Edelstein effect vanishes. Incorporating spin-orbit coupling tilts the momentum-space electronic spins into the $(k_x,k_y)$ plane and imparts finite in-plane components to the Edelstein response. Our findings highlight the Fe-based superconductors as platforms for exploring odd-parity magnetism both on its own and coexisting with unconventional superconductivity.

Layered compounds $R\mathrm{S}{\mathrm{b}}_2$ ($R$ = light rare earth), which first hosted the discovery of non-rivial topological fermions in nonmagnetic $\mathrm{La}\mathrm{S}{\mathrm{b}}_2$, offer an exceptional platform for probing the interplay between magnetism and topological electronic states. Through high-field magnetotransport measurements and first-principles calculations, we report colossal magnetoresistance up to $\sim 6\times {10}^3\%$ at 28 T and ultrahigh carrier mobility exceeding $1.5\times {10}^4\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at 2 K in magnetic $R\mathrm{S}{\mathrm{b}}_2$ with $R=\mathrm{Pr}$, Nd, and Sm. Analysis of Shubnikov–de Haas oscillations further reveals a nontrivial Berry phase, corroborating topologically protected quasiparticles. Our calculations confirm the existence of nearly fourfold degenerate Dirac-like flat bands that remain robust under applied magnetic field and spin-orbit coupling, providing the topological nature across this material family. These findings not only describe a compelling magnetic topological semimetal system, but also provide quantitative insights into how magnetic ordering interacts with and sustains nontrivial topological states.

We systematically investigate the emergence of electron crystal phases in rhombohedral multilayer graphene using comprehensive self-consistent Hartree Fock calculations combined with ab initio tight binding model. As the carrier density increases, we uncover an isospin cascade sequence of phase transitions that gives rise to a rich variety of ordered states, including electron crystal phases with nonzero Chern numbers. We further show the near degeneracy of these topological electron crystals hosting extended quantum anomalous Hall effect (EQAH) in the mean field regime and characterize pressure driven phase transitions. Finally, we discuss the thermodynamic signatures, particularly the behavior of the inverse compressibility, in light of recent experimental observations.

Materials with reduced dimensionality offer beneficial density-of-states (DOS) profiles for thermoelectric energy conversion, but can be impractical in realistic devices. Encouragingly, bulk high-symmetry materials can also exhibit similar quasi-low-dimensional band structures. A striking example is the full-Heusler compound ${\mathrm{Na}}_2\mathrm{TlSb}$, whose valence-band energy isosurfaces can form intersecting two-dimensional pockets, i.e., a boxlike structure. The individual energy isosurface sheets resemble those of 1D quantum wires. The combination of high electron velocities (perpendicular to the pockets) and a rapidly increasing DOS with energy in the transport regime (due to the low dimensionality) makes ${\mathrm{Na}}_2\mathrm{TlSb}$ a representative case where the band structure gives rise to attractive electronic transport properties. However, these beneficial features could be counteracted by high electronic scattering rates due to the large scattering space. In this first-principles study of ${\mathrm{Na}}_2\mathrm{TlSb}$, we find that the electronic scattering rates remain modest. This result is linked to the reduced matrix elements of large-momentum ($\mathbf{q}$) scattering across the delocalized energy isosurfaces. The enhanced free-carrier screening due to the large DOS also contributes to reducing scattering. In combination, the low-dimensional features and modest scattering result in excellent electronic transport properties. Combined with an ultralow lattice thermal conductivity of ${\kappa }_{\ell }<1\mathrm{W}/\mathrm{mK}$ reported in the literature, we predict a thermoelectric figure of merit ranging from 2.4 at 300 K to 4.4 at 600 K. The $n$-type properties are also favorable, with $zT$ values from 1.5 at 300 K to 3.0 at 600 K.

The interaction between a particle's spin and momentum—known as spin-orbit (SO) coupling—is the cornerstone of modern spintronics. In Bose-Einstein condensates of ultracold atoms, SO coupling can be implemented and precisely controlled experimentally; photonic systems, on the other hand, possess an intrinsic SO interaction because of the longitudinal-transverse splitting of the photon modes. In this work, we focus on such spinor, SO-coupled exciton-polariton condensates on a ring, where the strength of the synthetic magnetic field is controlled by the geometrical dimensions of the structure. Inspired by recent experiments, we investigate the dynamics of a weakly nonlinear four-mode bosonic Josephson junction within this geometry. We discover a narrow parameter range in which the interplay of the tunneling dynamics with polariton-specific SO coupling leads to a distinct regime, with dynamical switching of the fluid's circular polarization degree to the opposite, along the entire ring or on just one of its halves. Our results demonstrate polariton condensates in ring configurations as excellent candidates for all-optical controllable spin-switch applications, with prospects for scalability and observing nontrivial polarization patterns.

We investigate the nonequilibrium dynamics of charge density waves in a pumped one-dimensional Hubbard superlattice with staggered on-site Coulomb interactions at half filling, using time-dependent exact diagonalization. In equilibrium, the system exhibits commensurate charge correlations consistent with the superlattice periodicity. Under laser excitation, the charge correlation function exhibits distinct behaviors across four representative frequencies, spanning both linear and nonlinear optical regimes. Notably, we observe a laser-induced commensurate-to-incommensurate transition in the charge order, manifested by a shift in the peak wave vector of the charge structure factor. This transition is driven by sublattice-selective doublon-holon dynamics, where the laser frequency and intensity determine whether excitations predominantly destabilize the charge order on the weakly or strongly interacting sublattice. Our analysis of the excitation spectrum and site-resolved correlation dynamics reveals the underlying mechanisms of this transition. These results suggest a promising optical strategy for controlling charge order in superlattice-based quantum materials.

Hund's coupling plays a decisive role in shaping electron correlations of multi-orbital systems, giving rise to a class of materials—Hund's metals—that combine local-moment physics with metallic transport. Here, we derive an effective low-energy description of such a system near the Mott insulating regime, starting from the multi-orbital Hubbard-Kanamori Hamiltonian and projecting onto the high-spin manifold favored by Hund's first rule. The resulting Hund-projected Kanamori model captures the interplay between carrier motion and magnetic correlations in the presence of strong Hund's coupling. In the undoped limit, the model reduces to a spin-$N/2$ Heisenberg system with suppressed quantum fluctuations, approaching the classical limit for realistic five-band configurations. Upon doping, carrier motion couples strongly to the spin background and drives ferromagnetic correlations through a Hund-enhanced kinetic mechanism analogous to, but much stronger than, Nagaoka ferromagnetism. Owing to its reduced sign problem, the model can be addressed with advanced path-integral methods to determine quasiparticle structure and effective interactions between carriers—quantities that are challenging to obtain with other methods. This framework establishes a microscopic bridge between the Kanamori model and the emergent magnetic and transport phenomena characteristic of Hund's metals.

High-fluence silicon-28 (${}^{28}\mathrm{Si}$) ion implantation has been shown to produce isotopically enriched surface regions within natural silicon (Si) wafers through localized focused ion beam implantation. In this work, molecular dynamics simulations are performed to simulate ${}^{28}\mathrm{Si}$ ion implantations into a Si sample for insights into the enrichment process dynamics. We conduct a series of simulations to emulate the irradiation process at incident energies, ranging from 0.5 to 2 keV, and fixed angles of incidence of $0^{\circ }, 7^{\circ }$, and ${15}^{\circ }$. Our findings elucidate how implantation energy and angle of incidence affect sputter yield and enrichment levels. The outcomes of this study highlight the importance of atomistic simulations in providing a mechanistic understanding of deposition and sputtering for the optimization of the enrichment process. Moreover, comparisons with transmission electron microscopy images of natural silicon wafers enriched using focused ion beam performed by Acharya et al. [Commun. Mater. 5, 57 (2024)], show strong agreement for both postirradiated and postannealed configurations, further validating the simulation approach. This work will support future studies of isotopic enrichment of natural Si and the development of novel methods to fabricate spin-qubit devices for quantum computing architectures.

In this work, the spin-valley dependent transmission properties in magnetic superlattices (MSLs) based on monolayer transition metal dichalcogenides, especially tungsten diselenide ${\mathrm{WSe}}_2$, are studied. Ferromagnetic strips and top electrostatic gates are periodically distributed to generate the superlattice profiles, where the former induce the magnetic proximity effect in the two-dimensional material. Using the transfer matrix method, the spin-valley transmission channels are numerically calculated for parallel (PM) and antiparallel magnetization (AM). We calculate the Bloch wave vector to corroborate the transmission minibands and minigaps of MSLs. We obtain perfect valley polarization states for both PM and AM; however, well-defined spin polarization states are absent. When structural asymmetry is induced in MSLs, two well-defined spin-valley polarization states for both magnetization configurations are established. More importantly, these states can be accessed by switching the magnetization direction. As the period number increases the regions of perfect spin-valley polarization enhance and become broader. A TMR with negative values is obtained. The so-called anomalous transport characterized by a negative TMR is the result of the particular spin-valley splitting of the valence band. In short, magnetic ${\mathrm{WSe}}_2$ superlattices could be the basis for versatile devices with spin-valley polarization and magnetoresistive capabilities.

We investigate the topological phase diagram of an extension of the Haldane model with equal spin pairing superconductivity. In two dimensions, we find a topological nodal superconducting phase, which exhibits a chiral Majorana mode propagating along the edges of nanoribbons with cylindrical boundary conditions. This phase is however unstable in a finite two-dimensional rectangular-shaped lattice, yielding corner states close to zero energy in a flake with alternating zigzag and armchair edges. When we reduce one of the dimensions, quantum confinement gaps out the bulk bands faster than the edge states. In this scenario, hybridization between the edge states can then result in Majorana zero modes. Our results hence suggest quantum confinement as a crucial ingredient in building quasi-one-dimensional topological superconducting phases out of two-dimensional nodal topological superconductors. Furthermore, we characterize the emergence of this novel topological phase by means of its topological invariant, coinciding with a quantized conductance of $2e^2/h$ in a normal-superconducting junction.

The prediction of infrared dielectric function of strongly anharmonic crystals at elevated temperatures remains a nontrivial task. In this study, we target this challenge via Green-Kubo molecular dynamics based on a machine learning potential trained from first-principles data using LiF as a prototype material. The temperature-dependent infrared dielectric function and reflectance of LiF crystals in the range 295–840 K are predicted and show very good agreement with experimental results. We also demonstrate that the classical Lorentz model with input from perturbation theory deviates appreciably from the experiment at high temperatures, even considering the lattice expansion as well as both the third- and fourth-order anharmonicity. These findings highlight the machine learning molecular dynamics as an efficient approach in accurately capturing the physics of infrared optical response in strongly anharmonic materials.

The Jahn-Teller distortion and the resulting staggered orbital-ordering phenomena typically lead to ferromagnetism in perovskite-structured compounds. Herein, we demonstrate the role of strong Jahn-Teller distortion in explaining the ground-state structure and quasi-two-dimensional behavior of the fluoride perovskite ${\mathrm{CsMnF}}_4$. Despite its theoretical robustness, comprehensive experimental verification has remained incomplete in these fluoride perovskites. Hence, a comprehensive investigation combining both experimental and theoretical approaches was conducted on ${\mathrm{CsMnF}}_4$, which was synthesized $via$ a coprecipitation method in hydrofluoric acid. Structural characterization using variable-temperature synchrotron x-ray diffraction (SXRD) and neutron powder diffraction (NPD) confirmed a layered tetragonal framework. Thermal analysis revealed its phase stability and decomposition behavior. Magnetometry and temperature-dependent NPD measurements indicate long-range magnetic ordering below 20 K, with a ferromagnetic ground state confirmed through Curie-Weiss analysis and hysteresis studies. Complementary theoretical investigations provided insights into the magnetic structure and electronic properties, aligning well with experimental observations. Dynamical analysis of the undistorted prototype phase (i.e., $P4/mmm$), elucidated the underlying mechanism for the structural phase transitions in ${\mathrm{CsMnF}}_4$. We confirmed the experimentally observed distorted (i.e., $P4/n$) phase to be the stable phase, which is achieved by condensing a robust Jahn-Teller distortion mode coupled to two in-phase octahedral rotations along the $x$ and $y$ axes $\left(a^{+}{a}^{+}{c}^0\right)$. Our analysis reveals quasi-two-dimensional ferromagnetism with an estimated $T_c$ of 22 K and the spin-phonon coupling parameter $\lambda =2.25\mathrm{c}{\mathrm{m}}^{-1}$ associated with an $A_g$ phonon mode at $526.07\mathrm{c}{\mathrm{m}}^{-1}$. This work provides a complete experimental and theoretical insight into the structure-magnetism properties of ${\mathrm{CsMnF}}_4$, with theoretical insights shedding light on the structural phase transitions and quasi-two-dimensional ferromagnetism based on Jahn-Teller distortion.

Magnonics has emerged as a promising route toward next-generation information technologies beyond the scaling limits of Moore's law. Compared with the extensively studied yttrium iron garnet (YIG), thulium iron garnet (TmIG) has attracted growing interest for magnonics due to its ability to sustain robust perpendicular magnetic anisotropy (PMA). This work moves beyond the conventional strain-dominated picture of PMA by establishing a unified framework for magnetic anisotropy control in TmIG films, where epitaxial strain, oxygen vacancies, and cation stoichiometry are integrated as coupled factors. High-quality epitaxial TmIG films of varying thicknesses were deposited via magnetron sputtering on YSGG ($\eta =0.82\%$) and GGG ($\eta =0.49\%$) substrates. The results show that TmIG/YSGG films exhibit stable PMA, with the PMA strength reaching a maximum at 30 nm, whereas those grown on GGG exhibit dominant in-plane anisotropy because of insufficient tensile strain. Through a combination of transmission electron microscopy, magnetic characterization, and theoretical modeling, we further reveal that oxygen deficiency together with near-ideal cation stoichiometry enhances the effective magnetostriction coefficient $|{\lambda }_{111}|$ in TmIG/YSGG films, thereby strengthening the magnetoelastic contribution to PMA. These findings establish TmIG as a tunable PMA platform through coupled strain and defect chemistry, providing insights for engineering garnet-based magnonic materials.

$MA{\mathrm{N}}_3$ ($M$=V, Nb, Ta; $A$=Si, Ge) monolayers, intrinsic Janus materials derived from the $M{A}_2{\mathrm{N}}_4$ family, are known to be either in 1T phase or in 2H phase with polar characteristics. However, the exploration of phase space in two-dimensional (2D) $MA{\mathrm{N}}_3$ monolayers remains incomplete, and the discovery of new phases could further enrich the understanding of its structure-property relationships and expand its functional versatility. In this work, through systematic structural searches and stability evaluations, we have successfully identified a third phase in 2D $MA{\mathrm{N}}_3$ monolayers, hereafter referred to as the L phase, using first-principles calculations, and systematically investigated its structural, electronic, and magnetic properties. The results show that the L phase preserves intrinsic polarity while exhibiting pronounced composition-dependent polarization behavior. Compared with the 1T/2H phases, the polarization strengths of ${\mathrm{VSiN}}_3$ and ${\mathrm{VGeN}}_3$ in the L phase decrease, whereas those in ${\mathrm{NbGeN}}_3$ and ${\mathrm{TaGeN}}_3$ increase by more than a factor of 2. Based on these findings, the classification of low polarization state and high polarization state to describe the relative magnitude of polarization across different structural phases of the same material system is proposed. In addition, the L-$MA{\mathrm{N}}_3$ monolayers feature distinct flat bands near the valence band maximum, leading to a high density of states near the Fermi level. Upon hole doping, the systems exhibit emergent Stoner-type ferromagnetism and undergo a transition from nonmagnetic semiconductors to ferromagnetic half-metals. These findings provide a theoretical foundation and material candidates for polymorphic regulation and the design of spintronic devices in two-dimensional polar materials.