Quantum Relaxation and Metastability of Lattice Bosons with Cavity-Induced Long-Range Interactions

1/3 Power-Law Universality Class out of Stochastic Driving in Interacting Systems

In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.

Dynamical Transitions and Critical Behavior between Discrete Time Crystal Phases

In equilibrium physics, spontaneous symmetry breaking and elementary excitation are two concepts closely related with each other: the symmetry and its spontaneous breaking not only control the dynamics and spectrum of elementary excitations, but also determine their underlying structures. In this Letter, based on an exactly solvable model, we propose a phase ramping protocol to study an excitationlike behavior of a nonequilibrium quantum matter: a discrete time crystal phase with spontaneous temporal translational symmetry breaking. It is shown that slow ramping could induce a dynamical transition between two Z_{2} symmetry breaking time crystal phases in time domain, which can be considered as a temporal analog of the soliton excitation spatially sandwiched by two degenerate charge density wave states in polyacetylene. By tuning the ramping rate, we observe a critical value at which point the transition duration diverges, resembling the critical slowing down phenomenon in nonequilibrium statistic physics. We also discuss the effect of stochastic sequences of such phase ramping processes and its implication to the stability of the discrete time crystal phase against noisy perturbations.

Aging in the Long-Range Ising Model

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ=1.25 in the effectively short-range regime, while for stronger long-range interactions the data are consistent with λ=d/2=1. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.

Tunable and Robust Long-Range Coherent Interactions between Quantum Emitters Mediated by Weyl Bound States

Long-range coherent interactions between quantum emitters are instrumental for quantum information and simulation technologies, but they are generally difficult to isolate from dissipation. Here, we show how such interactions can be obtained in photonic Weyl environments due to the emergence of an exotic bound state whose wave function displays power-law spatial confinement. Using an exact formalism, we show how this bound state can mediate coherent transfer of excitations between emitters, with virtually no dissipation and with a transfer rate that follows the same scaling with distance as the bound state wave function. In addition, we show that the topological nature of Weyl points translates into two important features of the Weyl bound state, and, consequently, of the interactions it mediates: first, its range can be tuned without losing the power-law confinement, and, second, they are robust under energy disorder of the bath. To our knowledge, this is the first proposal of a photonic setup that combines simultaneously coherence, tunability, long range, and robustness to disorder. These findings could ultimately pave the way for the design of more robust long-distance entanglement protocols or quantum simulation implementations for studying long-range interacting systems.

Extended Bose-Hubbard Model with Cavity-Mediated Infinite-Range Interactions at Finite Temperatures

We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short- and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures. At a fixed chemical potential, we map out the distributions of the superfluid order parameters and number densities with respect to the temperatures. For a charge density wave, we find that the global-range interaction enhances the charge order by increasing the transition temperature at which the charge order melts out, while for a supersolid phase, we find that the disappearance of the charge order and the superfluid order occurs at different temperature. At a fixed number-density filling factor, we extract the temperature dependence of the thermodynamic functions such as internal energy, specific heat and entropy. Across the superfluid phase transition, the specific heat has a discontinuous jump.

Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks

Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices can lead to finite energies per site, which deserves attention. Here, we present a tensor network approach to construct the ground states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on constrained optimizations of their infinite matrix product states description, which contains no truncation step, offers a very simple mathematical structure, and other minor advantages at the cost of slightly higher polynomial complexity in comparison to an existing method. More precisely speaking, our proposed algorithm is in part equivalent to the more generic and well-established solvers of infinite density-matrix renormalization-group and variational uniform matrix product states, which are, in principle, capable of accurately representing the ground states of such infinite-range-interacting many-body systems. However, we employ some mathematical simplifications that would allow for efficient brute-force optimizations of tensor-network matrices for the specific cases of highly-symmetric infinite-size infinite-range models. As a toy-model example, we showcase the effectiveness and explain some features of our method by finding the ground state of the U(1)-symmetric infinite-dimensional antiferromagneticXXHeisenberg model.