Absence of thermalization in finite isolated interacting Floquet systems

Abstract

Conventional wisdom suggests that the long-time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal-entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy nonthermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit nonthermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have nonthermal average doublon densities. We show that this nonthermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.

Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain

“…These models can then shed light on periodically-driven systems, while describing experimentally-relevant situations [6][7][8], and being relevant in various fields of physics [1,9,10]. Previous works have explored some of these scenarios [11,12], and numerical studies have also been performed for non-integrable systems [13][14][15][16], where many-body resonances are of major interest [17][18][19][20][21][22][23].…”

Report on scipost_202005_00011v1

“…These models can then shed light on periodically-driven systems, while describing experimentally-relevant situations [6][7][8], and being relevant in various fields of physics [1,9,10]. Previous works have explored some of these scenarios [11,12], and numerical studies have also been performed for non-integrable systems [13][14][15][16], where many-body resonances are of major interest [17][18][19][20][21][22][23].…”

“…T from e −iHavT can strongly couple quasi-degenerate eigenstates [17][18][19][20][21][22][23]. These so-called Floquet resonances give rise to avoided crossings that result into the Floquet eigenstates being linear combinations of two such (near-) resonant states.…”

Suppression of Heating in Quantum Spin Clusters under Periodic Driving as a Dynamic Localization Effect

“…Yet, even in such a case, a practically important question remains concerning the size dependence of the DL effects. This question has also been discussed in the literature [34], but so far no quantitative criterion for the onset of dynamical localization as a function of the system size and the strength of the perturbation has been formulated. The present work aims at filling this gap.…”

“…It is also, possibly, the necessary condition[35]: In finite clusters with ergodic Hamiltonians, if the analog of our DL criterion is satisfied for lowtemperature states ϕ 0 , but high-temperature states are dynamically delocalized, then low-temperature states are still likely to "leak" to the high-temperature range due to the higher-order effects of the perturbations by H on not included in the second-order perturbation theory behind Eq.(3). In this scenario, the stronger tendency to DL at lower temperatures only delays the onset of normal heating during the prethermalization stage [34,[38][39][40][41][42][43][44].…”