The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the $1+1-$, $2+1-$, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area-law entanglement phase of the steady state. Our primary example is circuits with unitaries respecting a global Ising symmetry and two competing types of measurements. The phase diagram has an area-law phase with spin-glass order, which undergoes a direct transition to a paramagnetic phase with volume-law entanglement, as well as a critical regime. Using mutual information diagnostics, we find that such entanglement transitions preserving a global symmetry are in universality classes different from those without symmetry. We analyze generalizations of such hybrid circuits to higher dimensions, which allow for coexistence of order and volume-law entanglement, as well as topological order without any symmetry restrictions.

A pair-density-wave state has been suggested to exist in underdoped cuprate superconductors, with some supporting experimental evidence emerging over the past few years from scanning tunneling spectroscopy. Several studies have also linked the observed quantum oscillations in these systems to a reconstruction of the Fermi surface by a pair-density wave. Here, we show, using semiclassical analysis and numerical calculations, that a Fermi pocket created by first-order scattering from a pair-density wave cannot induce such oscillations. In contrast, pockets resulting from second-order scattering can cause oscillations. We consider the effects of a finite pair-density-wave correlation length on the signal, and demonstrate that it is only weakly sensitive to disorder in the form of $\pi$-phase slips. Finally, we discuss our results in the context of the cuprates and show that a bidirectional pair-density wave may produce observed oscillation frequencies.

We present a detailed analysis of the relaxation dynamics in an extended bosonic Josephson junction. We show that stochastic classical field simulations using Gross-Pitaevskii equations in three spatial dimensions reproduce the main experimental findings of Pigneur et al. [Phys. Rev. Lett. 120, 173601 (2018)]. We give an analytic solution describing the short time evolution through multimode dephasing. For longer times, the observed relaxation to a phase-locked state is caused by nonlinear dynamics beyond the sine-Gordon model, induced by the longitudinal confinement potential and persisting even at zero temperature. Finally, we analyze different experimentally relevant trapping geometries to mitigate these effects. Our results provide the basis for future experimental implementations aiming to study nonlinear and quantum effects of the relaxation in extended bosonic Josephson junctions.

In this work we are concerned with the understanding of the collisionless drag or entrainment between two superfluids, also called Andreev-Bashkin effect, in terms of current response functions. The drag density is shown to be proportional to the cross transverse current-current response function, playing the role of a normal component for the single-species superfluid density. We can in this way link the existence of finite entrainment with the exhaustion of the energy-weighted sum rule in the spin channel. The formalism is then used to reproduce some known results for a weakly interacting Bose-Bose mixture. We include the drag effect to determine the beyond mean-field correction on the speed of sound and on the spin dipole excitations for a homogeneous and a trapped weakly interacting gas, respectively. Finally, we show that the response to a quick dipole perturbation on one of the species induces a dipole moment on the other species which is proportional to the drag at short times.

We study superconductivity in a family of one-dimensional incommensurate systems with $s$-wave pairing interaction. The incommensurate potential can alter the spatial characteristics of electrons in the normal state, leading to either extended, critical, or localized wave functions. We find that superconductivity is significantly enhanced when the electronic wave function exhibits a critical multifractal structure. This criticality also manifests itself in the power-law dependence of the superconducting temperature on the pairing strength. As a consequence, an extended superconducting dome is expected to exist around the localization-delocalization transition, which can be induced by either tuning the amplitude of the incommensurate potential or by varying the chemical potential across a mobility edge. Our results thus suggest a different approach to enhance the superconducting transition temperature through engineering of the incommensurate potential.

We propose a class of lattice models realizable in a wide range of setups whose low-energy dynamics exactly reduces to Dirac fields subjected to ($1+1$)-dimensional [($1+1$)D] gravitational backgrounds, including (anti-)de Sitter space-time. Wave packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integrals $t\left(x\right)\propto x^{\gamma }$ when $\gamma \ge 1$, signaling the formation of black hole event horizons. For $\gamma <1$ instead the wave packets behave radically different and bounce off the horizon. We show that the eternal slowdown relates to a zero-energy spectral singularity of the lattice model and that the semiclassical wave packets trajectories coincide with the geodesics on ($1+1$)D dilaton gravity, paving the way for new and experimentally feasible routes to mimic black hole horizons and realize ($1+1$)D space-times as they appear in certain gravity theories.

We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets. It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from $\pm 1$ to zero. This gapful spin liquid state with zero Chern number is simply the toric code phase. Our result potentially explains the topological nematic transition recently observed in $\alpha \text{−}{\mathrm{RuCl}}_3$ via heat capacity measurements (O. Tanaka et al., arXiv:2007.06757).

The fundamental band gaps of liquid water and hexagonal ice are calculated through advanced electronic-structure methods. We compare specifically the performance of state-of-the-art $GW$ calculations with nonempirical hybrid functionals. For the latter, we fix the free parameters either through the dielectric response of the material or through enforcing Koopmans' condition to localized states. The various approaches yield consistent band gaps, in good agreement with available experimental references. Furthermore, we discuss the critical aspects of each approach that underlie the band-gap predictions.

Superconductivity in a crystalline lattice without inversion is subject to complex spin-orbit-coupling effects, which can lead to mixed-parity pairing and an unusual magnetic response. In this study, the properties of a layered superconductor with alternating Rashba spin-orbit coupling in the stacking of layers, hence (globally) possessing a center of inversion, is analyzed in an applied magnetic field, using a generalized Ginzburg-Landau model. The superconducting order parameter consists of an even- and an odd-parity pairing component which exchange their roles as dominant pairing channel upon increasing the magnetic field. This leads to an unusual kink feature in the upper critical field and a first-order phase transition within the mixed phase. We investigate various signatures of this internal phase transition. The physics we discuss here could explain the recently found $H\text{−}T$ phase diagram of the heavy-fermion superconductor $\mathrm{Ce}{\mathrm{Rh}}_2{\mathrm{As}}_2$.

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An excellent example of a controlled QPT is the field-induced ordering of a gapped quantum magnet. Although numerous “quasi-one-dimensional” coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-two-dimensional (2D) systems are special for multiple reasons. Motivated by the ancient pigment Han purple (${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of ${\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{CuSi}}_2{\mathrm{O}}_6$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the spin Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque, and magnetocalorimetric measurements with nuclear magnetic resonance studies near the QPT. With a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr substitution in Han purple.

We study the spectral statistics of spatially extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor $K\left(t\right)$ of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK Hamiltonian lower bounds the Thouless time $t_{\mathrm{Th}}$ of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK Hamiltonian in the continuum limit, which allows us to extract $t_{\mathrm{Th}}$. In particular, we analytically argue that in a system of length $L$ that conserves the $m\mathrm{th}$ multipole moment, $t_{\mathrm{Th}}$ scales subdiffusively as $L^{2(m+1)}$. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the $m\mathrm{th}$ multipole moment, $t_{\mathrm{Th}}$ has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems.

The fermion sign problem, when severe, prevents the computation of physical quantities of a system of interacting fermions via stochastic evaluation of its path integral. This is due to the oscillatory nature of the integrand $\exp (-S),$ where $S$ is the imaginary-time action. This issue is a major obstacle to first-principles lattice quantum Monte Carlo studies of excited states of electrons in matter. However, in the Kohn-Sham orbital basis, which is the output of a density-functional theory simulation, the path integral for electrons in a semiconductor nanoparticle has only a mild fermion sign problem and is amenable to evaluation by standard stochastic methods. This is evidenced by our simulations of silicon hydrogen-passivated nanocrystals such as ${\mathrm{Si}}_{35}{\mathrm{H}}_{36},{\mathrm{Si}}_{87}{\mathrm{H}}_{76},{\mathrm{Si}}_{147}{\mathrm{H}}_{100}$, and ${\mathrm{Si}}_{293}{\mathrm{H}}_{172},$ which range in size $1.0-2.4$ nm and contain 176 to 1344 valence electrons. We find that approximating the fermion action by its leading order polarization term results in a positive-definite integrand in the functional integral, and is a very good approximation of the full action. We compute imaginary-time electron propagators and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of previous high-precision $G_0{W}_0$ calculations. This formalism allows calculations of more complex excited states such as excitons and trions.

Topological Dirac and Weyl semimetals are currently attracting intense interest due to their exotic physical properties. Transition metal diarsenides such as ${\mathrm{MoAs}}_2$ and ${\mathrm{WAs}}_2$ have been reported to harbor very high magnetoresistance suggesting the possible existence of a topological quantum state, although this conclusion remains dubious. Here, using systematic angle-resolved photoemission spectroscopy (ARPES) measurements and parallel first-principles calculations, we discuss the electronic structures of ${\mathrm{TAs}}_2$ (T = Mo, W). Two different cleavage planes of ${\mathrm{MoAs}}_2$ are found to harbor distinctly different surface states. Our experiments show the presence of Dirac-like dispersions on the (001) plane, which our first-principles calculations ascribe to trivial surface states. Our in-depth study also finds ${\mathrm{WAs}}_2$ to possess a trivial electronic structure. Our study emphasizes the importance of identifying the cleavage plane in low-symmetry systems and indicates that topological semimetallic states are not the key for generating high magnetoresistance in ${\mathrm{MoAs}}_2$ and ${\mathrm{WAs}}_2$.

We theoretically study the lattice distortion induced first- and second-order topological phase transition in rectangular ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$ monolayer. When compressing the lattice constant in one direction, our first-principles calculation shows that the ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$ undergoes a band inversion at $\mathrm{\Gamma }$ point in a wide doping range, say $x\in (0.0,0.7)$, which indicates the first-order topological phase transition of its electronic band structure. Meanwhile, because the unidirectional pressure breaks ${\mathrm{C}}_4$ symmetry, the topological edge states along the (100) and (010) directions have different Dirac energy. Given the high-temperature superconductivity of ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$ monolayer, we found that the ${\mathrm{C}}_4$ symmetry breaking is essential to support Majorana corner states in either presence or absence of time-reversal symmetry. Especially in the case of breaking time-reversal symmetry, we can obtain a single Majorana zero mode at each corner without concerning the details of the superconducting pairing symmetries and applied Zeeman form, which can potentially bring advantages in the experimental implementation.

We explore the feasibility of optically forming long-range tetratomic and larger polyatomic molecules in their ground electronic state from ultracold pairs of polar molecules aligned by external fields. Depending on the relative orientation of the interacting diatomic molecules, we find that a tetratomic can be formed either as a weakly bound complex in a very extended halo state or as a pure long-range molecule composed of collinear or nearly collinear diatomic molecules. The latter is a novel type of tetratomic molecule comprised of two diatomic molecules bound at a long intermolecular range and predicted to be stable in cold and ultracold regimes. Our numerical studies were conducted for ultracold KRb and RbCs, resulting in the production of ${\left(\mathrm{KRb}\right)}_2$ and ${\left(\mathrm{RbCs}\right)}_2$ complexes, respectively. Based on universal properties of long-range interactions between polar molecules, we identify triatomic and tetratomic linear polar molecules with a favorable ratio of dipole and quadrupole moments for which the approach could be generalized to form larger polyatomic molecules.

We show that the resistivity plateau of ${\mathrm{SmB}}_6$ at low temperature, typically taken as a hallmark of its conducting surface state, can systematically be influenced by different surface treatments. We investigate the effect of inflicting an increasing number of handmade scratches and microscopically defined focused ion beam-cut trenches on the surfaces of flux-grown ${\mathrm{Sm}}_{1-x}{\mathrm{Gd}}_x{\mathrm{B}}_6$ with $x=0$ and 0.0002. Both treatments increase the resistance of the low-temperature plateau, whereas the bulk resistance at higher temperatures largely remains unaffected. Notably, the temperature at which the resistance deviates from the thermally activated behavior decreases with cumulative surface damage. These features are more pronounced for the focused ion beam treated samples, with the difference likely being related to the absence of microscopic defects such as subsurface cracks. Therefore, our method presents a systematic way of controlling the surface conductance.

We theoretically investigate the elusive Andreev-Bashkin collisionless drag for a two-component one-dimensional Bose-Hubbard model on a ring. By means of tensor network algorithms, we calculate the superfluid stiffness matrix as a function of intra- and interspecies interactions and of the lattice filling. We then focus on the most promising region close to the so-called pair-superfluid phase, where we observe that the drag can become comparable with the total superfluid density. We elucidate the importance of the drag in determining the long-range behavior of the correlation functions and the spin speed of sound. In this way, we are able to provide an expression for the spin Luttinger parameter $K_S$ in terms of drag and the spin susceptibility. Our results are promising in view of implementing the system by using ultracold Bose mixtures trapped in deep optical lattices, where the size of the sample is of the same order of the number of particles we simulate. Importantly, the mesoscopicity of the system, far from being detrimental, appears to favor a large drag, avoiding the Berezinskii-Kosterlitz-Thouless jump at the transition to the pair-superfluid phase which would reduce the region where a large drag can be observed.

We present a hydrodynamic theory to describe a chiral electron system with a Weyl spin-orbit interaction on a field-theoretic basis. Evaluating the momentum flux density as a linear response to a driving electric field, we derive an equation of motion for the orbital angular momentum. It is shown that the chiral nature leads to a dynamic bulk angular momentum generation by inducing a global torque as a response to the applied field. The steady-state angular momentum is calculated taking into account rotational viscosity.

Three-dimensional phase-contrast imaging of multiply-scattering samples in x-ray and electron microscopy is challenging due to small numerical apertures, the unavailability of wave front shaping optics, and the highly nonlinear inversion required from intensity-only measurements. In this work, we present an algorithm using the scattering matrix formalism to solve the scattering from a noncrystalline medium from scanning diffraction measurements and simultaneously recover the illumination aberrations. We demonstrate our method experimentally in a scanning transmission electron microscope, recovering the scattering matrix of a heterogeneous sample with two layers of multiwall carbon nanotubes filled with ${\mathrm{TaTe}}_2$ core-shell structures, spaced $10\mathrm{nm}$ apart in the axial direction. Our work enables phase contrast imaging and materials characterization in multiply-scattering samples at high resolution for a wide range of materials.