We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space.We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, manybody localized systems with quenched disorder remain localized at finite energy.We support our conclusions by numerical simulations of disordered spin chains.We argue that our results hold for general driving protocols, and discuss their experimental implications.

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, both in experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin chain model. We show that the resulting LIOMs are quasi-local, and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.Comment: 8 pages, 3 figure

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to non-equilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The non-equilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents-discussed in the seminal work by Kibble and Zurek-and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-N problems and prove their universality with respect to protocol choice. We also introduce a new protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to discrete symmetry protected order via the explicit examples of the Haldane phase of one dimensional spin chains and the topological Ising paramagnet in two dimensions. We comment on the challenge of extending these results to cases where the protecting symmetry is continuous.

A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.Introduction-Remarkable experimental advances in the construction and control of synthetic quantum systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14] have revived interest in foundational questions about quantum thermalization and the emergence of statistical mechanics [15][16][17]. Experiments have observed robust thermalization when the interactions are strong, localization and the concomitant persistence of initial state memory when spatial inhomogeneities are strong, and long-lived prethermal states near special integrable points [4][5][6][7][8][9][10][11][12][13][14].Conventional wisdom holds that generic, strongly interacting isolated systems quickly reach local thermal equilibrium at infinite temperature, irrespective of the initial state [15][16][17]. It therefore came as a surprise when recent quench experiments in long Rydberg-blockaded atomic chains reported a strong initial state dependence in infinite temperature thermalization times [12]. In the Rydberg-blockaded regime, the effective dynamics occurs in a constrained manifold as adjacent atoms cannot simultaneously support Rydberg excitations. The experiment observed long-lived coherent oscillations in local observables starting from a Neél state with the maximum number of Rydberg excitations (called |Z 2 ), but fast relaxation starting from a state with no Rydberg excitations (|0 ). What is the source of this coherence at infinite temperature?In this Rapid Communication, we provide a partial answer by identifying signatures of integrability in the Hamiltonian controlling the time-evolution (H 0 in Eq. (1)). Specifically, we construct a deformation of H 0 that both magnifies the amplitude and lifetime of the coherent oscillations observed in quenches, and monotonically enhances various spectral signatures of integrability. From our study, we hypothesize that a parent nonergodic point that is proximate in parameter space to H 0 controls its short-time dynamics and small system-size eigenspectra. This parent point is a new model in constrained systems that has not been previously studied; although it is exhibits various ...

Li and Haldane conjectured and numerically substantiated that the entanglement spectrum of the reduced density matrix of ground-states of time-reversal breaking topological phases (fractional quantum Hall states) contains information about the counting of their edge modes when the groundstate is cut in two spatially distinct regions and one of the regions is traced out. We analytically substantiate this conjecture for a series of FQH states defined as unique zero modes of pseudopotential Hamiltonians by finding a one to one map between the thermodynamic limit counting of two different entanglement spectra: the particle entanglement spectrum (PES), whose counting of eigenvalues for each good quantum number is identical to the counting of bulk quasiholes (up to accidental zero eigenvalues of the reduced density matrix), and the orbital entanglement spectrum (OES), considered by Li and Haldane. By using a set of clustering operators which have their origin in conformal field theory (CFT) operator expansions, we show that the counting of the OES eigenvalues in the thermodynamic limit must be identical to the counting of quasiholes in the bulk . The latter equals the counting of edge modes at a hard-wall boundary placed on the sample. Our results can be interpreted as a bulk-edge correspondence in entanglement spectra. Moreover, we show that the counting of the PES and OES is identical even for CFT states which are likely bulk gapless, such as the Gaffnian wavefunction.

We investigate the entanglement spectra arising from sharp real-space partitions of the system for quantum Hall states. These partitions differ from the previously utilized orbital and particle partitions and reveal complementary aspects of the physics of these topologically ordered systems. We show, by constructing one to one maps to the particle partition entanglement spectra, that the counting of the real-space entanglement spectra levels for different particle number sectors versus their angular momentum along the spatial partition boundary is equal to the counting of states for the system with a number of (unpinned) bulk quasiholes excitations corresponding to the same particle and flux numbers. This proves that, for an ideal model state described by a conformal field theory, the real-space entanglement spectra level counting is bounded by the counting of the conformal field theory edge modes. This bound is known to be saturated in the thermodynamic limit (and at finite sizes for certain states). Numerically analyzing several ideal model states, we find that the real-space entanglement spectra indeed display the edge modes dispersion relations expected from their corresponding conformal field theories. We also numerically find that the real-space entanglement spectra of Coulomb interaction ground states exhibit a series of branches, which we relate to the model state and (above an entanglement gap) to its quasiparticle-quasihole excitations. We also numerically compute the entanglement entropy for the ν = 1 integer quantum Hall state with real-space partitions and compare against the analytic prediction. We find that the entanglement entropy indeed scales linearly with the boundary length for large enough systems, but that the attainable system sizes are still too small to provide a reliable extraction of the sub-leading topological entanglement entropy term.

The quantum O(N ) model in the infinite N limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of N in varying spatial dimensions (d > 1). Here we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late time state could be inferred from the finite temperature phase diagram. In the infinite N limit, we show that not only does the model not lead to equilibration on account of an infinite number of conserved quantities, it also does not relax to a generalized Gibbs ensemble (GGE) consistent with these conserved quantities. Instead, an infinite number of new conservation laws emerge at late times and the system relaxes to an emergent GGE consistent with these. Nevertheless, we still find that the late time states following quenches bear strong signatures of the equilibrium phase diagram. Notably, we find that the model exhibits coarsening to a non-equilibrium critical state only in dimensions d > 2, that is, if the equilibrium phase diagram contains an ordered phase at non-zero temperatures.