Periodically driven ergodic and many-body localized quantum systems

Abstract

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.

Discrete Time Crystals: Rigidity, Criticality, and Realizations

“…In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20]. Under certain conditions, however, prethermal time-crystal-like dynamics can persist for long times [21,22] even in the absence of localization before ultimately being destroyed by thermalization [18,23].…”

“…Subsequent work developed more precise definitions of such time translation symmetry breaking (TTSB) [6][7][8] and ultimately led to a proof of the "absence of (equilibrium) quantum time crystals" [9]. However, this proof leaves the door open to TTSB in an intrinsically out-of-equilibrium setting, and pioneering recent work [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10-13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a sub-harmonic response for physical observables.An important constraint on symmetry breaking in many-body Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17][18]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20].…”

“…An important constraint on symmetry breaking in many-body Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17][18]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20].…”

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

“…An exciting possibility is to obtain a topologically nontrivial steady state for an interacting, periodically driven system [15][16][17]19,20]. The common wisdom dictates that a periodically driven system with dispersive modes is doomed to evolve into a highly random state that is essentially an infinite temperature state as far as any finite-order correlation functions are concerned [51,[59][60][61][62][63]. Our results on the single-particle level demonstrate that it is possible to obtain a topological Floquet spectrum with no delocalized states away from the edges of the system.…”

Observation of a discrete time crystal

“…The robust subharmonic synchronization of the many-body Floquet system is the essence of the discrete time crystal phase [7][8][9][10] . In a DTC, the underlying Floquet drive should generally be accompanied by strong disorder, leading to manybody localization 13 and thereby preventing the quantum system from absorbing the drive energy and heating to infinite temperatures [14][15][16][17] .…”