We study the inverse Faraday effect (IFE) in a Dirac Hamiltonian with random impurities using Keldysh formalism and diagrammatic perturbation theory. The mass term in the Dirac Hamiltonian is essential for IFE, where the spin magnetic moment induced by circularly polarized light is proportional to the frequency of the incident light within the THz regime. For massive Dirac electrons, the corrections due to short-range impurities on spin magnetic moment vertex exhibits mixing of the spin magnetic moment vertex and spin angular momentum vertex. The spin magnetic density response is divergently enhanced by the vertex corrections near the band edge, indicting a long-range diffusion of spin density profile in massive Dirac electrons.

We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in $2+1$ dimensions. TDP is defined as the constant correction that appears in the ground-state expectation value of a partial symmetry transformation applied to a connected spatial region $M$, the absolute value of which scales generically as $exp(-\alpha l+\gamma )$ where $l$ is the perimeter of $M$ and $\gamma$ is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that $e^{\gamma }$ can be related to the quantum dimension of the symmetry defect, and provide a general formula for $\gamma$ when the entanglement Hamiltonian of the topological phase can be described by a ($1+1$)-dimensional conformal field theory (CFT). A special case of TDP is equivalent to the topological Rényi entanglement entropy when the symmetry is the cyclic permutation of the replica of the gapped phase. We then investigate several examples of lattice models of topological phases, both analytically and numerically, in particular when the assumption of having a CFT edge theory is not satisfied. We also consider an example of partial translation symmetry in Wen's plaquette model and show that the result can be understood using the edge CFT. Our results establish an alternative tool to detect quantum topological order.

We introduce alternative statistical mechanics expressions for thermoelastic properties of monatomic crystals, in the classical canonical ensemble, using the mapped-averaging framework. Two reference models are examined as a basis for the coordinate mapping: ideal gas (IG) and quasiharmonic (QH) crystal. The former prescribes affine mapping and yields the conventional expressions for the properties, while the latter has, in addition, a nonaffine component and yields alternative formulas, denoted as “harmonically mapped averaging” (HMA). While the (strain-dependent) affine mapping is universal and does not require system-specific information, the HMA method uses a system- (and strain-) dependent matrix to specify the mapping; this mapping matrix is derived from the force-constant matrix of the QH reference and its variation with strains. In practice, implementing HMA (and affine) schemes depends on the availability of analytical (Lagrangian) derivatives of potential energy with respect to strains (e.g., Born term) and coordinates (e.g., Hessian matrix); however, when these derivatives are unavailable, numerical derivatives can be computed via finite difference by moving atoms according the mapping matrices, while straining the crystal. In no circumstances does mapped averaging affect sampling of configurations; it involves only the calculation of averages. Results show that HMA provides CPU speedup ranging from a factor of 4, to over two orders of magnitude, compared to the conventional formulas (especially at low temperature), with the best performance obtained with isotropic-deformation properties. In addition to its application to molecular simulation, HMA can open avenues for developing new theories for thermoelastic properties.

We study the nonequilibrium dynamics of two-dimensional planar ion Coulomb crystals undergoing a structural buckling transition to a three-plane configuration, driven by a reduction of the transverse confining frequency. This phase transition can be theoretically modeled using a mapping to a two-dimensional Ginzburg-Landau theory with a complex order parameter field. We demonstrate that finite rate quenches result in the creation of stable topological vortices, which are localized point regions around which the phase of the order parameter field winds a multiple of $2\pi$. The density of the defects as a function of quench rate is investigated using molecular dynamics simulations, and its scaling is shown to be consistent with Kibble-Zurek theory of defect formation. Following the quench, the annihilation of vortex and antivortex pairs results in the relaxation of defect density that follows a diffusive scaling with a logarithmic correction. This paper highlights the potential for investigating complex nonequilibrium statistical physics of topological defects in an experimentally accessible ion trap setting.

We investigate the indirect magnetic exchange interaction between two magnetic moments in a two-dimensional semiconductor with quartic dispersion, featuring a singularity at the band edge. We obtain the Green's functions analytically to calculate the magnetic exchange interaction at zero temperature. We show that the singularity in the density of states (DOS) for quartic dispersion gives rise to an enhancement in the amplitude of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction as the Fermi energy is swept toward the band edge. Furthermore, a region of finite exchange interaction arises, with a range increasing as the Fermi energy approaches the band edge. The results lay the possibility of an electrical/chemical control over the exchange interactions.

The Hall anomaly, as appears in the mixed-state Hall resistivity of type-II superconductors, has been the subject of numerous theories, but there is not yet a consensus on its origin. In this paper, we conduct a quantitative analysis of the magnetotransport measurements on ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}{\mathrm{CaCu}}_{2.0}{\mathrm{O}}_{8+\delta }$ (BSCCO) thin films by Zhao et al. [Phys. Rev. Lett. 122, 247001 (2019)] and validate a previously proposed vacancy mechanism [cf. Ao, J. Phys. Condens. Matter. 10, L677 (1998)] with many-body vortex correlations for the phenomenon. The model attributes the Hall anomaly to the motion of vacancies in pinned fragments of the vortex lattice. Its validity is first examined by an exploration of the vortex states near the Kosterlitz-Thouless transition on the vortex crystal. Comparisons are then carried out between the measured activation energies with the calculated creation energy of the vortex-antivortex pair and the vacancy energy on the flux-line lattice, with no adjustable parameter. Our analysis elucidates the theoretical basis and prerequisites of the vacancy model. In particular, the vacancy activation energies are an order of magnitude smaller than that of a sole vortex line. The proposed mechanism may provide a macro-theoretical framework for other studies.

${\mathrm{LaH}}_{10}$ exhibits the near-room-temperature superconductivity, but the high fabrication pressure exceeding 200 GPa limits the possibility of its experimental research and application. To examine the feasibility of high-temperature superconductivity at ambient pressure in light-element compounds, we study the crystal structure, metallization, and electron-phonon interaction of $M{\left(\mathrm{BN}\right)}_5$ ($M$ = La and Y) with ${\mathrm{LaH}}_{10}$-like clathrate configuration, based on the first-principles calculations. The result shows that adopting B and N to substitute H, the strong $s{p}^3$ hybridization between B and N greatly reduces the pressure to keep the dynamical stability. We predict that the strong electron-phonon coupling exists in $M{\left(\mathrm{BN}\right)}_5$ and the $T_c$ values of $\mathrm{La}{\left(\mathrm{BN}\right)}_5$ and $\mathrm{Y}{\left(\mathrm{BN}\right)}_5$ reach 69 and 59 K at ambient pressure, respectively. As a result, the high-temperature superconductivity at ambient pressure in clathrate BN compounds has been proved theoretically, which provides a way to lower the work pressure of hydride superconductors.

The transverse folding algorithm [M. C. Bañuls et al., Phys. Rev. Lett. 102, 240603 (2009)] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can overcome the limitations of matrix product states when entanglement grows slower in the time than in the space direction. We present a contraction strategy that makes use of the exact light cone structure of the tensor network representing the observables. The strategy can be combined with the hybrid truncation proposed for global quenches by Hastings and Mahajan Phys. Rev. A 91, 032306 (2015), which significantly improves the efficiency of the method. We demonstrate the performance of this transverse light cone contraction also for transport coefficients, and discuss how it can be extended to other dynamical quantities.

${\mathrm{PbTaSe}}_2$ is a unique topological material, in which the number of nodal lines is expected to change at the structural transition between the lower-temperature/pressure L phase and the higher-temperature/pressure H phase. We report the anomalous Nernst effect attributed to the Berry curvature of nodal lines and its change with the structural transition. In the L phase, the Nernst coefficient ($S_{yx}$) shows a steplike magnetic field dependence reminiscent of the anomalous Nernst effect of nonmagnetic Dirac/Weyl semimetals. By applying hydrostatic pressure, we discovered that the amplitude of the anomalous component markedly decreases at the transition to the H phase, which might correspond to the partial annihilation of nodal-line structures.

The insulating rare-earth magnet ${\mathrm{LiY}}_{1-x}{\mathrm{Ho}}_x{\mathrm{F}}_4$ has received great attention because a laboratory field applied perpendicular to its crystallographic $c\mathrm{axis}$ converts the low-energy electronic spin Hamiltonian into the (dilute) transverse field Ising model. The mapping between the real magnet and the transverse field Ising model is strongly dependent on the exact nature of the low-energy Hamiltonian for the material, which can be determined by spectroscopy in the dilute limit. The energies of the eigenstates are in the difficult terahertz (THz) regime, and here we use THz time domain and Fourier transform spectroscopy to directly measure the lowest crystal-field levels of ${\mathrm{LiY}}_{1-x}{\mathrm{Ho}}_x{\mathrm{F}}_4$ in the dilute limit, including nuclear hyperfine substructure. The high resolution of our measurements allows us to observe the nonequidistantly spaced Ho ($I=\frac{7}{2}$) hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal-field parameters and extract the dipolar and quadrupolar hyperfine constants $A_J=0.02703\pm 0.00003$ ${\text{cm}}^{-1}$ ($810.3\pm 0.9$ MHz) and $B=0.04\pm 0.01$ ${\text{cm}}^{-1}$($1.2\pm 0.3$ GHz), respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the ${}^{5}I_8$ ground-state manifold, including the (nonlinear) hyperfine corrections. The latter improve the prediction precision by a factor of 60 compared to previous crystal-field parameters. Additionally, we establish the far-infrared, low-temperature refractive index of ${\mathrm{LiY}}_{1-x}{\mathrm{Ho}}_x{\mathrm{F}}_4$.

The possibility of “orbitally selective Mott transitions” within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion $U_1$ is insulating and another orbital, to which it is hybridized, with small $U_{-1}$, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the coexistence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a “Holstein-metal interface” where the electron-phonon coupling, $\lambda$, is zero in the “metallic” layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization $t_3$, but decreases and eventually vanishes as $t_3$ grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at an intermediate ratio of inter- to intralayer hopping strengths, $1.4\lesssim t_3/t\lesssim 3.4$. This is consistent with the occurrence of an “orbitally selective CDW” regime at weak $t_3$ in which the layer with ${\lambda }_1\ne 0$ exhibits long-range charge order, but the “metallic layer” with ${\lambda }_{-1}=0$, to which it is hybridized, does not.

This work studies the impact of the nonparabolicity on the formation of multisubband plasmons. We explore three semiclassical optical response models and compare their predictions to temperature-dependent absorption measurements from three structures: all doped GaAs/AlGaAs quantum wells with continuously varied parabolic binding potentials. We show that qualitative improvement in the prediction of the plasmon absorption peak can only be obtained by including both the energy and wave-function dependence on the in-plane wave vector. Our model, developed to include both these dependencies, uses a $\vec{k}·\vec{p}$-derived current density operator (instead of the usual scalar effective mass one). The model should be readily generalizable to a wide set of nanostructures, such as asymmetric half-parabolic wells or narrow band materials nanostructures beyond the quasi-Kohn regime.

Shiba bands formed by overlapping Yu-Shiba-Rusinov subgap states in magnetic impurities on a superconductor play an important role for realizing topological superconductors. Here, we theoretically demonstrate the existence of topological gapless Shiba bands on a magnetically doped $s$-wave superconducting surface with Rashba spin-orbit coupling in the presence of a weak in-plane magnetic field. Such bands develop from gapped Shiba bands through Lifshitz phase transitions accompanied by second-order quantum phase transitions for the intrinsic thermal Hall conductance. We also find a mechanism in Shiba lattices that protects the first-order quantum phase transitions for the intrinsic thermal Hall conductance. Due to the long-range hopping in Shiba lattices, the topological Shiba metal exhibits intrinsic thermal Hall conductance with large nonquantized values. As a consequence, there emerges a large number of second-order quantum phase transitions.

We present a multiscale density functional theory (DFT) informed molecular dynamics and tight-binding approach to capture the interdependent atomic and electronic structures of twisted bilayer graphene. We calibrate the flat band magic angle to be at ${\theta }_{\mathrm{M}}=1.{08}^{\circ }$ by rescaling the interlayer tunneling for different atomic structure relaxation models as a way to resolve the indeterminacy of existing atomic and electronic structure models whose predicted magic angles vary widely between $0.9^{\circ }$ and $1.3^{\circ }$. The interatomic force fields are built using input from various stacking and interlayer distance-dependent DFT total energies including the exact exchange and random phase approximation ($\mathrm{EXX}+\mathrm{RPA}$). We use a Fermi velocity of ${\upsilon }_{\mathrm{F}}\simeq {10}^6$ m/s for graphene that is enhanced by $\sim 15\%$ over the local density approximation (LDA) values. Based on this atomic and electronic structure model we obtain high-resolution spectral functions comparable with experimental angle-resolved photoemission spectroscopy. Our analysis of the interdependence between the atomic and electronic structures indicates that the intralayer elastic parameters compatible with the DFT-LDA, which are stiffer by $\sim 30\%$ than widely used reactive empirical bond order force fields, can combine with $\mathrm{EXX}+\mathrm{RPA}$ interlayer potentials to yield the magic angle at $\sim 1.{08}^{\circ }$ without further rescaling of the interlayer tunneling.

Superconducting spin qubits, also known as Andreev spin qubits, promise to combine the benefits of superconducting qubits and spin qubits defined in quantum dots. While most approaches to control these qubits rely on controlling the spin degree of freedom via the supercurrent, superconducting spin qubits can also be coupled to each other via the superconductor to implement two-qubit quantum gates. We theoretically investigate the interaction between superconducting spin qubits in the weak tunneling regime and concentrate on the effect of spin-orbit interaction (SOI), which can be large in semiconductor-based quantum dots and thereby offers an additional tuning parameter for quantum gates. We find analytically that the effective interaction between two superconducting spin qubits consists of Ising, Heisenberg, and Dzyaloshinskii-Moriya interactions and can be tuned by the superconducting phase difference, the tunnel barrier strength, or the SOI parameters. The Josephson current becomes dependent on SOI and spin orientations. We demonstrate that this interaction can be used for fast controlled phase-flip gates with a fidelity >99.99%. We propose a scalable network of superconducting spin qubits which is suitable for implementing the surface code.

The interplay of spin-orbit coupling (SOC) with the other energy scales gives rise to various novel and interesting quantum phenomena in the Ir based double perovskites. In recent findings the double-perovskites ${\mathrm{Sr}}_2{\mathrm{FeIrO}}_6$ (SFIO) and ${\mathrm{Ca}}_2{\mathrm{FeIrO}}_6$ (CFIO) have been reported to fall under the category of a SOC driven antiferromagnetic (AFM) Mott insulator. Using density functional theory based first principles calculations, we have performed a comparative electronic structure investigation of these compounds. We reveal the microscopic origin of the difference in the AFM transition temperature observed in the experiments through the calculated exchange interactions and the Wannier functions. We addressed the role of SOC in dictating the ground state properties of these two compounds. Although both of the compounds are isoelectronic and isovalent, however, the effective strength and the impact of SOC is very different and nonmonotonic in these compounds, due to the delicate balance with the other energy scales. Our study advances the understanding of the nontrivial role of SOC in driving ground state magnetic properties of the Ir based oxides in general and explores the opportunities for further designing of the SOC driven quantum phases.

Nonlinear responses in condensed matter have attracted recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses are often closely related to the multiband nature of the system, which can be taken into account by the geometric quantities such as the Berry curvature, as shown in the nonlinear Hall effect. Theoretically, the semiclassical Boltzmann treatment or the reduced density matrix method have often been employed, in which the effect of dissipation is included through the relaxation time approximation. In the diagrammatic method, the relaxation is treated through the imaginary part of the self-energy of the Green's function and the consequent broadening of the spectral function for the integration over the real frequency. Therefore, the poles of the Green's function do not play an explicit role when there is finite dissipation. In this paper, in stark contrast to the conventional picture, we show that the poles of the Green's function mainly determine the nonlinear response functions with dissipation, which leads to the terms with the Fermi distribution function of complex argument and results in the dissipation-induced geometric term. Furthermore, we elucidate the geometric origin of the nonreciprocal conductivity, which is related to the Berry curvature generalized to the higher derivative. Finally, we derive analytical results on the geometric terms of the nonlinear conductivities in type-I and type-II Weyl Hamiltonians to demonstrate their crucial roles.

Dynamical quantum impurities in metals induce electronic correlations in real space that are difficult to simulate due to their multiscale nature, so that only $s\text{−}\mathrm{wave}$ scattering in clean metallic hosts has been investigated so far. However, screening clouds should show anisotropy due to lack of full rotational invariance in two- and three-dimensional lattices, while inherent disorder will also induce spatial inhomogeneities. To tackle these challenges, we present an efficient and robust algorithm based on the recursive generation of natural orbitals defined as eigenvectors of the truncated single-particle density matrix. This method provides well-converged many-body wave functions on lattices with up to tens of thousands of sites, bypassing some limitations of other approaches. The algorithm is put to the test by investigating the charge screening cloud around an interacting resonant level, both on clean and disordered lattices, achieving accurate spatial resolution from short to long distances. We thus demonstrate strong anisotropy of spatial correlations around an adatom in the half-filled square lattice. Taking advantage of the efficiency of the algorithm, we further compute the disorder-induced distribution of Kondo temperatures over several thousands of random realizations, at the same time gaining access to the full spatial profile of the screening cloud in each sample. While the charge screening cloud is typically shortened due to the polarization of the impurity by the disorder potential, we surprisingly find that rare disorder configurations preserve the long-range nature of Kondo correlations in the electronic bath.

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its phase diagram in the interplane hopping $t_{\perp }$ versus on-site interaction $U$ parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small $U$. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our paper demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

High-order harmonic generation (HHG) in topological insulators (TIs) is receiving tremendous attention due to the topologically protected surface states. To study the HHG in topological surface, an open-boundary Su-Schrieffer-Heeger model was adopted and we rigorously addressed quantum decoherence via Lindblad equation. We find that role of the symmetry breaking is significant for HHG in TIs. Our results reveal that (i) the edge electrons in TIs radiate pure even-order harmonics via distinguishing the topological bulk and edge contributions; (ii) a short dephasing time makes the even-order harmonic yields lower than that of odd order; (iii) two-channel subcycle interference model and dynamics-symmetry analysis were developed to explain the odd- and even-order characteristic of HHG spectra; (iv) the symmetry breaking selectively enhances emission of certain channel. This work reveals the vital role of the TIs' symmetry in the strong-field HHG, which provides an alternative way to understand and control the HHG from topological surfaces.