5 research outputs found
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, , 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