Onset of Floquet Thermalisation

In presence of interactions, a closed, homogeneous (disorder-free) many-body system is believed to generically heat up to an `infinite temperature' ensemble when subjected to a periodic drive: in the spirit of the ergodicity hypothesis underpinning statistical mechanics, this happens as no energy or other conservation law prevents this. Here we present an interacting Ising chain driven by a field of time-dependent strength, where such heating onsets only below a threshold value of the drive amplitude, above which the system exhibits non-ergodic behaviour. The onset appears at {\it strong, but not fast} driving. This in particular puts it beyond the scope of high-frequency expansions. The onset location shifts, but it is robustly present, across wide variations of the model Hamiltonian such as driving frequency and protocol, as well as the initial state. The portion of nonergodic states in the Floquet spectrum, while thermodynamically subdominant, has a finite entropy. We find that the magnetisation as an {\it emergent} conserved quantity underpinning the freezing; indeed the freezing effect is readily observed, as initially magnetised states remain partially frozen {\it up to infinite time}. This result, which bears a family resemblance to the Kolmogorov-Arnold-Moser theorem for classical dynamical systems, could be a valuable ingredient for extending Floquet engineering to the interacting realm.Comment: 10 pages, including Supplemental Materia

Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws

Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities (LCQ) is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant "conservation laws" in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics has a much richer structure due to the existence of {\it emergent} conservation laws: these are approximate but stable conservation laws arising {\it due to the drive}, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp ergodicity threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This opens up a new possibility of stable Floquet engineering in such systems. This review intends to give a theoretical overview of these developments. We conclude by briefly surveying the experimental scenario.Comment: Invited Review for Journal of Physics: Condensed Mattte

Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems

Quantum phase transitions are central for the understanding of the equilibrium low-temperature properties of quantum matter. Locating them can be challenging both by means of theoretical techniques as well as for experiments. Here, we show that the antithetic strategy of forcing a system strongly out of equilibrium can provide a route to identify signatures of quantum phase transitions. By quenching a quantum chaotic (nonintegrable) spin chain, we find that local observables can exhibit distinct features in their intermediate-time dynamics, when the quench parameter is close to its critical value, where the ground state undergoes a quantum phase transition. We find that the effective temperature in the expected thermal-like states after equilibration exhibits a minimum in the vicinity of the quantum critical value of the quench parameter, correlating with the features in the real-time dynamics of observables. We also explore dynamical nonequilibrium signatures of a quantum critical point in a model with a topological transition, and discuss how to access our results experimentally in systems of Rydberg atoms

Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems

International audienceQuantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters. Accurately locating those transitions is challenging experimentally and theoretically. Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions. Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains. Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points. We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions

Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws

We consider a clean quantum system subject to strong periodic driving. The existence of a dominant energy scale, $h_D^x$, can generate considerable structure in an effective description of a system which, in the absence of the drive, is non-integrable, interacting, and does not host localization. In particular, we uncover points of freezing in the space of drive parameters (frequency and amplitude). At those points, the dynamics is severely constrained due to the emergence of an almost exact local conserved quantity, which scars the {\it entire} Floquet spectrum by preventing the system from heating up ergodically, starting from any generic state, even though it delocalizes over an appropriate subspace. At large drive frequencies, where a na\"ive Magnus expansion would predict a vanishing effective (average) drive, we devise instead a strong-drive Magnus expansion in a moving frame. There, the emergent conservation law is reflected in the appearance of an `integrability' of an effective Hamiltonian. These results hold for a wide variety of Hamiltonians, including the Ising model in a transverse field in {\it any dimension} and for {\it any form of Ising interactions}. The phenomenon is also shown to be robust in the presence of {\it two-body Heisenberg interactions with any arbitrary choice of couplings}. Further, we construct a real-time perturbation theory which captures resonance phenomena where the conservation breaks down, giving way to unbounded heating. This opens a window on the low-frequency regime where the Magnus expansion fails.Comment: 24 Pages (including Appendix