We study analytically and numerically the formation of bound states in the continuum (BICs) in quantum-mechanical and optical spatially symmetric multimode waveguide systems. The widely used Friedrich-Wintgen model predicts a BIC for two (nearly) degenerate eigenstates of the resonator. However, numerical calculations typically show that BICs may appear away from the degeneracy point (or avoided crossing region) in the energy-parameter space. From the two-mode point of view based on the Friedrich-Wintgen model, such BICs can be considered as accidental. In this paper, we go beyond the two-mode approximation and, appealing to the notion of intermode bound states, provide an illustrative procedure for deriving conditions for BIC formation within an arbitrary finite-mode approximation. In particular, we show that a three-mode approximation allows the description of a continuous transition of a BIC between different pairs of modes, which can be associated with it within the two-mode model. Also, a manifestation of exceptional points as (anti)resonance coalescence is discussed. Analytical conclusions are verified by the results of numerical simulations of two-dimensional quantum-mechanical and optical stubbed waveguides with confining impurities in the stub. Moreover, numerical simulations confirm the existence of BICs in optical subwavelength resonators, which were earlier predicted in quantum-mechanical waveguides.

Topological phase transitions involving intrinsic topological orders are usually characterized by qualitative changes of ground state quantum entanglement, which cannot be described by conventional mean-field theories with local order parameters. Here, we apply the lattice Chern-Simons theory to study frustrated quantum magnets and show that the conventional concepts, such as the order parameter and symmetry breaking, can still play a crucial role in certain topological phase transitions. The lattice Chern-Simons representation establishes a nonlocal mapping from quantum spin models to interacting spinless Dirac fermions. We show that breaking certain emergent symmetries of the fermionic theory could provide a unified approach to describing both magnetic and topological orders, as well as the topological phase transitions between them. We apply this method to the perturbed spin-1/2 $J_1-J_2$ XY model on the honeycomb lattice and predict a nonuniform chiral spin liquid ground state in the strong frustration region. This is further verified by our high-precision tensor network calculations. These results suggest that the lattice Chern-Simons theory can simplify the complicated topological phase transitions to effective mean-field theories in terms of fermionic degrees of freedom, which lead to different understandings that help to understand the frustrated quantum magnets.

The phenomenological theory for the polar instability giving rise to a two-dimensional electron gas at perovskite interfaces is hereby extended to include the coupling to perovskite tilts. A Landau theory for homogeneous tilts is first explored, setting the scene for the further, more realistic Landau-Ginzburg theory describing varying tilt amplitudes across a thin film. The theory is also generalized to account for the response to an applied electric field normal to the interface, which allows a finer control on phase transitions. The conventionally described physics of a single metal-insulator transition is substantially enriched by the coupling, the model describing various scenarios with one or two transitions, possibly continuous or discontinuous. First-principles calculations permit the estimation of the parameters defining the model, which have been calculated for the interface between lanthanum aluminate and strontium titanate.

Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.

A clear separation of the timescales governing the dynamics of “slow” and “fast” degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange coupled to a tight-binding system of (fast) conduction electrons. The effective equations of motion are derived under the constraint that the quantum state of the electron system at any instant of time $t$ lies in the $n$-dimensional low-energy subspace for the corresponding spin configuration at $t$. The effective low-energy theory unfolds itself straightforwardly and takes the form of a non-Abelian gauge theory with the gauge freedom given by the arbitrariness of the basis spanning the instantaneous low-energy sector. The holonomic constraint generates a gauge-covariant spin-Berry curvature tensor in the equations of motion for the classical spins. In the non-Abelian theory for $n>1$, opposed to the $n=1$ adiabatic spin dynamics theory, the spin-Berry curvature is generically nonzero, even for time-reversal-symmetric systems. Its expectation value with the representation of the electron state is gauge invariant and gives rise to an additional geometrical spin torque. Aside from anomalous precession, the $n\ge 2$ theory also captures the spin nutational motion, which is usually considered as a retardation effect. This is demonstrated by proof-of-principle numerical calculations for a minimal model with a single classical spin. Already for $n=2$ and in parameter regimes where the $n=1$ adiabatic theory breaks down, we find good agreement with results obtained from the full (unconstrained) theory.

A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic skyrmions. In the continuum approximation, this model reduces to a nonlinear sigma model on a squashed sphere that has a natural interpolating parameter. At one limit of the parameter, the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to hopfions, and in the other limit, it becomes very similar to the 3D Skyrme model. To better understand the relation between hopfions and 3D skyrmions, a model interpolating between the Faddeev-Niemi and the Skyrme models is reconsidered and it is shown that energies of the solitons obey a linear Bogomol'nyi-Prasad-Sommerfeld bound. The 3D skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.

Ergodicity breaking is observed in the blockade regime of Rydberg atom arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations which propagate entanglement. Evidence of nonlocal entanglement is found, showing that these nonthermal chaotic states may be useful to quantum computation.

Ferromagnetic honeycomb systems are known to exhibit a magnonic topological phase under the existence of the next-nearest-neighbor Dzyaloshinskii-Moriya interaction (DMI). Motivated by the recent progress in the sublattice-specific control of magnetic anisotropy, we study the topological phase of magnon bands of a honeycomb ferromagnetic monolayer and a bilayer with sublattice symmetry breaking due to the different anisotropy energy in the presence of the DMI. We show that there is a topological phase transition between the topological magnon insulator and the topologically trivial magnon phase driven by the change of the relative size of the DMI and the anisotropy differences between the sublattices. The magnon thermal Hall conductivity is proposed as an experimental probe of the magnon topology.

We study magnetization switching in the dynamical regime for in-plane magnetized systems, useful for field-free spin-orbit torque switching devices. We derive a formula for the switching probability, characterized by the thermal stability factor, critical current density, and the linewidth of ferromagnetic resonance. The formula agrees well with numerical simulations based on the Landau-Lifshitz-Gilbert equation. To study the viability of the theory developed, the switching probability of an in-plane magnetized ferromagnet in three-terminal spin-orbit torque switching devices is measured. We find that the transition width of the switching probability versus current increases with decreasing pulse width. The shape of the probability density, the current derivative of the switching probability, changes with varying pulse width. These characteristics are in good agreement with the theory developed. From the analyses, we show that the dynamical and thermally activated switching regimes can be distinguished simply from the shape of the probability density. The formula therefore provides useful means to analyze the switching probability of two-terminal spin torque and three-terminal spin-orbit torque switching devices.

Nonlocal tunneling spectroscopy of multiterminal semiconductor-superconductor hybrid devices is a powerful tool to investigate the Andreev bound states below the parent superconducting gap. We examine how to exploit both microscopic and geometrical symmetries of the system to extract information on the normal and Andreev transmission probabilities from the multiterminal electric or thermoelectric differential conductance matrix under the assumption of an electrostatic potential landscape independent of the bias voltages, as well as the absence of leakage currents. These assumptions lead to several symmetry relations on the conductance matrix. Next, by considering a numerical model of a proximitized semiconductor wire with spin-orbit coupling and two normal contacts at its ends, we show how such symmetries can be used to identify the direction and relative strength of Rashba versus Dresselhaus spin-orbit coupling. Finally, we study how a voltage-bias-dependent electrostatic potential as well as quasiparticle leakage breaks the derived symmetry relations and investigate characteristic signatures of these two effects.

The hybrid semiconductor-superconductor nanowire is expected to serve as an experimental platform to support Majorana zero modes. By rederiving its effective Kitaev model with spins, we discover a topological phase diagram, which assigns a more precise constraint on the magnetic field strength for the emergence of Majorana zero modes. We find that the effective pairing strength dressed by the proximity effect exhibits a significant dependence on the magnetic field, and thus the topological phase region is refined into a closed triangle in the phase diagram with chemical potential vs Zeeman energy (which is obviously different from the open hyperbolic region known before). This prediction is confirmed again by an exact calculation of quantum transport, where the zero bias peak of $2e^2/h$ in the differential conductance spectrum, as the necessary evidence for the Majorana zero modes, disappears when the magnetic field grows too strong. Therefore, the hybrid nanowire system does not support Majorana zero modes under a too strong magnetic field. For illustrations with practical hybrid systems, in the InSb nanowire coupled to NbTiN, the accessible magnetic field range is around 0.1–1.5 T; when coupled to an aluminum shell, the accessible magnetic field range should be smaller than 0.12 T. Our predictions are essential to significantly narrow down the range of magnetic fields for further searching Majorana zero modes in experiments.

We study electronic, charge, and magnetic properties of twisted bilayer graphene with fillings $2\le n\le 6$ per moire unit cell within the recently introduced formulation of extended dynamical mean-field theory for two-sublattice systems. We use previously obtained hopping parameters between the states, described by Wannier functions, centered at the lattice spots of AB and BA stacking, and the long-range Coulomb interaction, obtained within cRPA analysis. We show that account of spin exchange between AB and BA nearest-neighbor spots is crucial to introduce charge and spin correlations between these spots. The account of this exchange yields preferable concentration of electrons in the same valley, with the tendency of parallel spin alignment of electrons in AB and BA spots, in agreement with earlier results of the strong-coupling analysis, suggesting SU(2)$\times \mathrm{SU}$(2) emergent spin-valley symmetry. The local spectral functions show an almost gapped state at fillings $n=2,4,6$, and incoherent metal state for the other fillings. We find that in both cases the local states of electrons have rather long lifetimes. At the same time, the nonlocal charge and spin susceptibilities, obtained within the ladder approximation, are peaked at incommensurate wave vectors, which implies that the above-discussed ordering tendencies are characterized by an incommensurate pattern.

Half-metallic ferromagnets (HMFs) are one of the most promising materials in the field of spintronics due to their unique band structure, consisting of one spin subband having metallic characteristics along with another subband with semiconductor-like behavior. In this work, we report the synthesis of a novel quaternary Heusler alloy—FeMnVAl—and we have studied the structural, magnetic, transport, and electronic properties complemented with first-principles calculations. Among different possible structurally ordered arrangements, the optimal structure is identified by theoretical energy minimization. The corresponding spin-polarized band-structure calculations indicate the presence of a half-metallic ferromagnetic ground state. A detailed and careful investigation of the x-ray diffraction data, Mössbauer spectra, and nuclear magnetic resonance spectra suggests the presence of site disorder between the Fe and Mn atoms in the stable ordered structure of the system. The magnetic susceptibility measurement clearly establishes a ferromagnetic-like transition below $\sim 213$ K. The $\mathrm{Fe}$ Mössbauer spectrometry measurements suggest that only the Mn spins could be responsible for the magnetic order, which is consistent with our theoretical calculation. Surprisingly, the density-functional-theory calculations reveal that the spin-polarization value is almost immunized (92.4% $\to$ 90.4%) from the Mn-Fe structural disorder, even when nonmagnetic Fe and moment-carrying Mn sites are entangled inseparably. The robustness of spin polarization and half-metallicity in the studied FeMnVAl compound comprising structural disorder is thus quite interesting and could provide a new direction to investigate and understand the exact role of disorders on spin polarization in this class of materials, beyond the available knowledge.

At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultracold atoms, frustrated magnets, and quantum moiré materials, their unbiased presence remains elusive in microscopic two-dimensional lattice models. Here, we show, by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $\pi$-flux square lattice subjected to plaquette Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and a columnar valence bond solid at finite interaction and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected quantum states reside in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization, and the dynamic coupling between emergent matter and gauge fields and will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

Antiferromagnetic (AFM) and high ferroelectric (FE) orderings coexist in the pristine ${\mathrm{BiFeO}}_3$. However, its performance is suppressed by complex FE switching originated from its R3c space group and high leakage current due to the volatile nature of Bi. We theoretically predict that the performance can be enhanced by (B,F) codoping. To this end, ${\mathrm{BiFeO}}_3$ and its Ba-doped, ${\mathrm{Bi}}_{1-x}{\mathrm{Ba}}_x{\mathrm{FeO}}_{3-x/2}$, as well as (Ba,F) multidoped, ${\mathrm{Bi}}_{1-x}{\mathrm{Ba}}_x{\mathrm{FeO}}_{3-x}{\mathrm{F}}_x$, are analyzed structurally, magnetically, optically, and electrically for the pure (doped) compound (compositions), where $x=0.25$. The analyses are performed in the framework of density functional theory accompanied by random phase approximation, Berry phase theory, and Hubbard model using $\mathrm{PBE}\text{−}\mathrm{GGA}+U$ with $U_{\text{eff}}=4\left(5\right)\text{eV}$. Here, we predict that the tetragonal polar distortions of the co-doped compound with an AFM ordering lead to a nonzero spontaneous polarization. Hence, both the magnetic and electric polarizations coexist in the codoped composition. To assess the accuracy of the results, we calculate the spontaneous polarization for the pure ${\mathrm{BiFeO}}_3$ in both the $R3c$ and $P4mm$ symmetries and find the results in agreement with the available experimental and theoretical data. Furthermore, our dielectric functions for the pure case are found consistent with the experimental data. Moreover, absorption coefficient spectra, as calculated by $\mathrm{GGA}+U$ with $U_{\text{eff}}=4\text{eV}$ and TB-mBJ with its self-consistently converged $c=1.38$ parameter, using Tauc method also reveal direct optical gaps of 2.66 and 2.80 eV, which agree with the corresponding experimental optical gap of 2.74 eV. To study the impacts of doping on the intrinsic ferroelectricity improvement of ${\mathrm{BiFeO}}_3$, we then calculate and analyze the optical absorption edges and loss functions for the pristine and doped compounds. By taking the band structure, partial densities of states, energy loss function, and parallel component of the imaginary part of the dielectric tensor, $\Im \left[{\varepsilon }_{\parallel }\right]$, for the pure case into consideration simultaneously, the energies of the prominent peaks for $\Im \left[{\varepsilon }_{\parallel }\right]$ spectra and their corresponding permitted absorption (emission) transitions are rigorously analyzed and determined. The analyses reveal that the sources of the prominent peaks occurred in $\Im \left[{\varepsilon }_{\parallel }\right]$ mainly originate from the excitation states of the bound electrons of O $2s$, O $2p$, Bi $6s$, Bi $6p$, Fe $3d$, and Fe $4s$ orbitals. Our results in most of the energy ranges show that the intrinsic ferroelectricity can be improved by the (Ba,F) codoping due to the reduction of the leakage current achieving from the calculated electric energy loss function. Further, the rhombohedral ($R3c$) is changed by the codoping to the tetragonal ($P4mm$) structure with more convenient symmetry for polarization switching. Hence, the system not only remains multiferroic after the codoping, but also its performance is enhanced. These evidences show that the codoping can play a key role for the applications of this multiferroic system in various devices.

Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. In this work, we that, by adding topological frustration, an antiferromagnetic $XYZ$ spin chain, characterized by a discrete local symmetry, develops a region in parameter space that mimics the features of models with continuous symmetries. For instance, frustration closes the mass gap and we describe a continuous crossover between ground states with different quantum numbers, a finite (Fermi) momentum for low energy states, and the disappearance of the finite order parameter. Moreover, we observe nontrivial ground-state degeneracies, nonvanishing chirality, and a singular foliation of the ground-state fidelity. Across the boundary between this chiral region and the rest of the phase diagram, any discontinuity in the energy derivatives vanishes in the thermodynamic limit.

We study the exactly solvable one-dimensional model: the dimerized $XY$ chain with uniform and staggered transverse fields, equivalent upon fermionization to the noninteracting dimerized Kitaev-Majorana chain with modulation. The model has three known gapped phases with local and nonlocal (string) orders, along with the gapless incommensurate (IC) phase in the $U\left(1\right)$ limit. The criticality is controlled by the properties of zeros of model's partition function, analytically continued onto the complex wave numbers. In the ground state they become complex zeros of the spectrum of the Hamiltonian. The analysis of those roots yields the phase diagram which contains continuous quantum phase transitions and weaker singularities known as disorder lines (DLs) or modulation transitions. The latter are shown to occur in two types: DLs of the first kind with continuous appearance of the IC oscillations, and DLs of the second kind corresponding to a jump of the wave number of oscillations. The salient property of zeros of the spectrum is that the ground state is shown to be separable (factorized), and the model is disentangled on a subset of the DLs. From analysis of those zeros we also find the Majorana edge states and their wave functions.

We construct a dimerized square-octagon lattice model with the staggered magnetic fluxes threading plaquettes and find two types of topological states at half filling, i.e., the Chern insulator (CI) and the zero-Chern-number topological (ZCNT) states. The CI can be characterized on the basis of the chiral edge states and nonzero Chern number. Different from the CI, this ZCNT state hosts robust edge states with zero Chern number. Its topological nature can be identified by the quantized bulk polarization. More intriguingly, corner states emerge in this ZCNT state, even though its edge state is gapless. In addition, we present a phase diagram by tuning the dimerized hopping potential and the staggered fluxes. Our findings provide a promising approach to search more topological phases without time-reversal symmetry.