We present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with $M$ sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, $U$, and the total number of particles, $N$, from a single training. This approach bypasses the need to solve a new Hamiltonian for each different set of values $(U,N)$ and generalizes well even for out-of-distribution $(U,N)$. Using HubbardNet, we identify the two ground-state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the Hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice Hamiltonians.

A frozen, solid helium core, dubbed a snowball, is typically observed around cations in liquid helium. Here we discover, using path integral simulations, that around a cationic molecular impurity, protonated methane, the ${}^4\mathrm{He}$ atoms are indeed strongly localized akin to snowballs but still participate in vivid bosonic exchange induced by the rovibrational motion of the impurity. Such a combination of solidlike order with pronounced superfluid response in the first helium shell indicates that manifestations of local supersolid behavior of ${}^4\mathrm{He}$ can be induced by charged molecules.

By combining experiments and numerical simulations which model the dynamics of shaken atomic Bose-Einstein condensates, we reveal the surprising nature of quantum turbulence in these systems. Unlike the tangles of vortex lines described in the superfluid helium literature, we find that our turbulent atomic condensate contains a mixture of strong fragmented density fluctuations and small random vortex loops which are not homogeneously distributed. This unusual form of turbulence, with its own properties and scaling behavior, which we call strong quantum turbulence, is significantly different from the turbulence which is observed in either classical or other quantum systems, thus posing a new challenge in turbulence research.

We consider a configuration of three stacked graphene monolayers with commensurate twist angles ${\theta }_{12}/{\theta }_{23}=p/q$, where $p$ and $q$ are coprime integers with $0<p<\left|q\right|$ and $q$ can be positive or negative. We study this system using the continuum model in the chiral limit when interlayer coupling terms between ${\text{AA}}_{12}$ and ${\text{AA}}_{23}$ sites of the moiré patterns 12 and 23 are neglected. There are only three inequivalent displacements between the moiré patterns 12 and 23, at which the three monolayers' Dirac zero modes are protected. Remarkably, for these displacements and an arbitrary $p/q$ we discover exactly flat bands at an infinite set of twist angles (magic angles). We provide theoretical explanation and classification of all possible configurations and topologies of the flat bands.

Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this paper, we propose a tensor-network solvable model that allows us to tune between different symmetry enriched topological (SET) phases. Concretely, we consider a decorated two-dimensional toric code model for which the ground state can be expressed as a two-dimensional tensor-network state with bond dimension $D=3$ and two tunable parameters. We find that the time-reversal (TR) symmetric system exhibits three distinct phases: (i) an SET toric code phase in which anyons transform nontrivially under TR, (ii) a toric code phase in which TR does not fractionalize, and (iii) a topologically trivial phase that is adiabatically connected to a product state. We characterize the different phases using the topological entanglement entropy and a membrane order parameter that distinguishes the two SET phases. Along the phase boundary between the SET toric code phase and the toric code phase, the model has an enhanced $U\left(1\right)$ symmetry and the ground state is a quantum critical loop gas wavefunction whose squared norm is equivalent to the partition function of the classical $O\left(2\right)$ model. By duality transformations, this tensor-network solvable model can also be used to describe transitions between SET double-semion phases and between ${\mathbb{Z}}_2\times {\mathbb{Z}}_2^T$ symmetry protected topological phases in two dimensions.

Ultrafast pump-probe experiments can reveal the physics of complex materials by triggering a reaction with short laser pulses and then looking for the response. However, the repetition rate in such experiments is limited because the sample needs to cool down back to the initial state between subsequent laser excitations. Here we investigate by theory and experiment how this cooling rate depends on the shape and dimensionality of the material. Using $\mathrm{V}{\mathrm{O}}_2$ as the example, a strongly correlated material with an ultrafast phase transition with large latent heat, we report more than six orders of magnitude of change between the cooling times of freestanding thin films, thin films on a substrate, and bulk materials. A numerical latent-heat model reproduces all results and can therefore be generally used to predict the speed of the back reaction in almost all kinds of phase-change materials.

Skyrmions are topological solitons in two-dimensional systems and have been observed in various physical systems. Generating and controlling skyrmions in artificial resonator arrays lead to novel acoustic, photonic, and electric devices, but it is a challenge to implement a vector variable with the chiral exchange interaction. Here, we propose to use quadrature variables, where their parametric coupling enables skyrmions to be stabilized. A finite-element simulation indicates that an acoustic skyrmion would exist in a realistic structure consisting of a piezoelectric membrane array.

Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation facilitates the description of a discrete quantum spin system in terms of a continuous classical model and recasts the quantum spin effects within the framework of path integrals in a double $1/s$ and $\hslash s$ expansion, where $s$ is the magnitude of the spin. In particular, it allows for a much more direct path to the low- and high-temperature limits of the quantum system and to the definition of effective classical Hamiltonians that describe both thermal and quantum fluctuations. In this formalism, the quantum properties of the spins emerge as an effective anisotropy. We use atomistic spin dynamics to sample the path integral, calculate thermodynamic observables, and show that our effective classical models can reproduce the thermal expectation values of the quantum system within temperature ranges relevant for studying magnetic ordering.

Using first-principles calculations we model the out-of-plane switching of local dipoles in ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ (CIPS) that are largely induced by Cu off-centering. Previously, a coherent switching of polarization via a quadruple-well potential was proposed for these materials. In the supercells we considered, we find multiple structures with similar energies but with different local polar order. Our results suggest that the individual dipoles are weakly coupled in-plane, and under an electric field at very low temperatures these dipoles in CIPS should undergo incoherent disordered switching. The barrier for switching is determined by the single Cu-ion switching barrier. This in turn suggests a scale-free polarization with a switching barrier of $\sim 203.6$–258.0 meV, a factor of five smaller than that of ${\mathrm{HfO}}_2$ (1380 meV), a prototypical scale-free ferroelectric. The mechanism of polarization switching in CIPS is mediated by the switching of each weakly interacting dipole rather than the macroscopic polarization itself as previously hypothesized. These findings reconcile prior observations of a quadruple well with sloping hysteresis loops, large ionic conductivity even at 250 K, well below the Curie temperature (315 K), and a significant wake-up effect where the macroscopic polarization is slow to order and sets in under an applied electric field. We also find that computed piezoelectric response and the polarization show a linear dependence on the local dipolar order. This is consistent with having scale-free polarization and other polarization-dependent properties and opens doors for engineering tunable metastability by design in CIPS (and related families of materials) for neuromorphic applications.

Green's functions of non-Hermitian systems play a fundamental role in various dynamical processes. Because non-Hermitian systems are sensitive to boundary conditions due to the non-Hermitian skin effect, open-boundary Green's functions are closely related to the non-Bloch band theory. While the exact formula of open-boundary Green's functions in single-band non-Hermitian systems proves to be an integral along the generalized Brillouin zone (GBZ), the proper generalization in generic multiband systems remains unclear. In this paper, we derive a formula of open-boundary Green's functions in multiband non-Hermitian systems by viewing the multiband GBZ on the Riemann surface. This formula can be applied to describe directional amplification in multiband systems, which can be verified at various experimental platforms.

Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this paper, we rigorously address this issue and put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analog, the integral contribution, and a term that fully resolves the microstructure, the lattice contribution. For any system dimension, for any lattice, for any power-law interaction, and for linear, nonlinear, and multiatomic lattices, we show that the lattice contribution can be described by a differential operator based on the multidimensional generalization of the Riemann zeta function, namely, the Epstein zeta function. We employ our representation in Fourier space to solve the important problem of long-range interacting unconventional superconductors. We derive a generalized Bardeen-Cooper-Schrieffer gap equation and find emerging exotic phases in two-dimensional superconductors with topological phase transitions. Finally, we utilize nonequilibrium Higgs spectroscopy to analyze the impact of long-range interactions on the collective excitations of the condensate. We show that the interactions can be used to fine tune the Higgs mode's stability, ranging from exponential decay of the oscillation amplitude up to complete stabilization. By providing a unifying framework for long-range interactions on a lattice, both classical and quantum, our research can guide the search for exotic phases of matter across different fields.

We consider a one-dimensional driven-dissipative exciton-polariton condensate under incoherent pump, described by the stochastic generalized Gross-Pitaevskii equation. It was shown that the condensate phase dynamics maps under some assumptions to the Kardar-Parisi-Zhang (KPZ) equation, and the temporal coherence of the condensate follows a stretched exponential decay characterized by KPZ universal exponents. In this paper, we determine the main mechanisms, which lead to the departure from the KPZ phase, and identify three possible other regimes: (i) a soliton-patterned regime at large interactions and weak noise, populated by localized structures analog to dark solitons; (ii) a vortex-disordered regime at high noise and weak interactions, dominated by point-like phase defects in space-time; and (iii) a defect-free reservoir-textured regime where the adiabatic approximation breaks down. We characterize each regime by the space-time maps, the first-order correlations, the momentum distribution and the density of topological defects. We thus obtain the phase diagram at varying noise, pump intensity and interaction strength. Our predictions are amenable to observation in state-of-art experiments with exciton-polaritons.

We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar order, and an attractive dimer-dimer interaction $v$ between two adjacent dimers that lie on the same principal axis of the lattice. The Monte Carlo simulations of finite size systems rely on our grand-canonical generalization of the dimer worm algorithm, while the tensor network computations are based on a uniform matrix product ansatz for the eigenvector of the row-to-row transfer matrix that work directly in the thermodynamic limit. The phase diagram has nematic, columnar order and fluid phases, and a nonzero temperature multicritical point at which all three meet. For any fixed $v/u<\infty$, we argue that this multicritical point continues to be located at a nonzero hole fugacity $z_{\mathrm{mc}}(v/u)>0$; our numerical results confirm this theoretical expectation but find that $z_{\mathrm{mc}}(v/u)\to 0$ very rapidly as $v/u\to \infty$. Our numerical results also confirm the theoretical expectation that the corresponding multicritical behavior is in the universality class of the four-state Potts multicritical point on critical line of the two-dimensional Ashkin-Teller model.

The coexistence in the low-temperature spin-conducting phases of the zigzag materials ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ and ${\mathrm{SrCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ of one-dimensional (1D) physics with important deviations from it is not well understood. The studies of this paper account for an important selection rule that follows from interchain spin states being coupled more strongly within the spin dynamical structure factor of such zigzag materials whenever they are connected by a specific symmetry operation of the underlying lattice. In the case of excited states, this symmetry operation is only a symmetry in spin space if $no$ electronic spin flip is performed within the generation of such states. The corresponding selective interchain couplings both protect the 1D physics and are behind important deviations from it concerning the enhancement of the spectral-weight intensity of $S^{zz}(k,\omega )$. Strong evidence is provided that this justifies, beyond interchain mean-field theory and in contrast to 1D physics, the experimental low-energy dominance in both zigzag materials of the longitudinal nuclear magnetic resonance relaxation rate term $1/T_1^{\parallel }$ for the whole magnetic field interval of the spin-conducting phases. To further understand the role of selective interchain couplings concerning their contradictory effects in protecting the 1D physics and controlling deviations from it, the physical-spins scattering processes behind the experimentally observed sharp peaks in the dynamic structure factor components are investigated. Indeed, the experimentally observed Bethe strings in $S^{+-}(k,\omega )$ cannot be expressed in terms of configurations of usual spinons. We find that the line shape at and near the sharp peaks of the spin dynamic structure factor experimentally observed in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ and ${\mathrm{SrCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ is fully controlled by unbound-unbound and unbound-bound scattering of singlet pairs of physical spins $1/2$. Our results on both the role of selective interchain couplings in protecting the 1D physics and being behind deviations from it and on the dynamical properties being controlled by scattering of singlet pairs of physical spins $1/2$ open the door to a key advance in the understanding of the physics of the spin chains in ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ and ${\mathrm{SrCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$.

Bound states in continuum (BICs) are states of a system possessing significantly large lifetimes with applications across various branches of science. In this work, we propose an expedient protocol to engineer BICs using the Kerr nonlinearities of a system which otherwise has no BICs. The generation of BICs is a direct artifact of the nonlinearity and the associated expansion in the dimensionality of the system. In particular, we consider single- and two-mode anharmonic systems and provide a number of solutions apposite for the creation of BICs. The nonlinearity-induced BICs can be controlled by external drive. In close vicinity to the BIC, the steady state response of the system is immensely sensitive to perturbations in natural frequencies of the system, and we illustrate its propitious sensing potential in the context of experimentally realizable setups for both optical and magnetic nonlinearities.

An orbital current can be generated whenever an object has a translational degree of freedom and a rotational degree of freedom. In condensed matter physics, intra-atomic contributions to the transverse orbital transport, labeled the orbital Hall effect, rely on propagating wave packets that must consist of hybridized atomic orbitals. However, interatomic contributions have to be considered as well because they give rise to an alternative mechanism for generating orbital currents. As we show, even wave packets consisting purely of $s$ electrons can transport orbital angular momentum if they move on a cycloid trajectory. We introduce the kagome lattice with a single $s$ orbital per atom as the minimal model for the orbital Hall effect and observe the cycloid motion of the electrons in the surface states.

Illumination has been long known to affect semiconductor defect properties during either growth or operating processes. Current theories of studying the illumination effects on defects usually have the assumption of unaffected formation energies of neutral defects as well as defect transition energy levels, and use the quasi-Fermi levels to describe behaviors of excess carriers with conclusions at variance. In this work, we first propose a method to simulate steady illumination conditions, based on which we demonstrate that formation energies of neutral defects and defect transition energy levels are insensitive to illumination. Then, we show that optical and thermal excitation of electrons can be seen equivalent with each other to reach a steady electron distribution in a homogeneous semiconductor. Consequently, the electron distribution can be characterized using just one effective temperature $T^{\prime }$ and one universal Fermi level $E_F^{{}^{\prime }}$ for a homogeneous semiconductor under continuous and steady illuminations, which can be seen as a combination of quasiequilibrium electron system with $T^{\prime }$ and a lattice system with $T$. Using these concepts, we uncover the universal mechanisms of illumination effects on charged defects by treating the band-edge states explicitly on the same footing as the defect states. We find that the formation energies of band-edge “defect” states shift with increased $T^{\prime }$ of electrons, thus affecting the $E_F^{{}^{\prime }}$, changing defect ionic probabilities, and affecting concentrations of charged defects. We apply our theory to study the illumination effects on the doping behaviors in GaN:Mg and CdTe:Sb, obtaining results in accordance with experimental observations. More interesting experimental defect-related phenomena under steady illuminations are expected to be understood from our theory.

Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate quantized Hall conductances, associated with topology both in the single particle and the strongly correlated many-body limit. Interestingly, the topology of the integer effect can be realized in superconducting multiterminal systems, but a proposal for the more complex fractional counterpart is lacking. In this work, we theoretically demonstrate how to achieve fractional quantized transconductance in an engineered chain of Josephson junctions. Crucially, similar to the stabilization of the conductance plateaus in Hall systems by disorder, we obtain stable transconductance plateaus as a result of nonadiabatic Landau-Zener transitions. We furthermore show that the fractional plateaus are robust to disorder and study the optimal operation regime to observe these effects. Our proposal paves the way for quantum simulation of exotic many-body out-of-equilibrium states in Josephson junction systems.

Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would manifest at noninteger dimension. Here, we report on the appearance of fractal eigenvalue degeneracies and Fermi surfaces in Hermitian and non-Hermitian topological band structures. This might have profound implications on the physics of black holes and Fermi surface instability driven phenomena, such as superconductivity and charge density waves.