Fate of dynamical many-body localization in the presence of disorder

Abstract

Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here, we show that, although any randomness in the interactions of a many body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale τ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down (τ shoots up) by orders of magnitude as the ratio of the drive frequency ω and amplitude h0 tends to certain specific values (the freezing condition). If ω is increased while maintaining the ratio h0/ω at a fixed freezing value, then τ diverges exponentially with ω. The results can be easily extended for a larger family of disordered fermionic and bosonic systems.The dynamics of quantum systems driven out of equilibrium by coherent periodic drives has remained an intriguing topic of interest from the early days of quantum mechanics (see, e.g., [1]) to date [2-28]. One interesting and well-known phenomenon in this field, where repeated quantum interference results in a scenario which is quite counter-intuitive and unexpected from the classical point of view, is that of dynamical freezing in a quantum system under a periodic drive. Illustrious examples include the localization of a single quantum particle for all time while being forced periodically in free space (dynamical localization [29]), or in one of the two wells of a doublewell potential modulated sinusoidally (coherent destruction of tunneling [30]). In both cases, this happens due to the coherent suppression of tunneling.A many-body version of this phenomenon, dubbed as dynamical many-body freezing, has also been observed both theoretically [31][32][33][34][35][36] and experimentally [26]. Dynamical many-body freezing, however, is a more drastic version of dynamical localization: in the latter only the tunneling term is renormalized to zero by the external drive, resulting in localization in real space, while in the former the entire many-body Hamiltonian -with all its mutually non-commuting terms -vanishes [31]. This implies freezing of any arbitrary initial state in the Hilbert space, rather than freezing of initial states localized in real space only. Intuitively, such an unequivocal freezing of all degrees of freedom of a many-body system seems possible only under very special circumstances, where certain simplicities in the structure of the Hamiltonian allow for such large-scale destructive quantum interference. Here, we demonstrate that such dynamical manybody freezing can have strong manifestations even in a system where dynamics is induced by interactions which are totally random.The plan of the paper is as follows. After introducing the system and the drive, we briefly sketch the content of our analytical a...

Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

“…[46]. Therefore the scaling behaviors similar to the ones studied in the present work can be seen in these systems as well (e. g. the scaling of the decay time with drive parameters [46]). …”

“…It is interesting to notice that the effective long-range interaction of spins can be generated in periodically driven interacting systems [26,[45][46][47] as a part of effective Hamiltonian as suggested in Ref. [46].…”

Effects of local periodic driving on transport and generation of bound states

“…Systems exhibiting dynamical localization include driven two-level systems 1 , classical and quantum kicked rotors [65][66][67][68][69] , the Kapitza pendulum 70,71 , and bosons in an optical lattice 72 . It has been shown that remnants of dynamical localization may survive even in the presence of strong disorder 73 . In an earlier paper, it was shown that a combination of interactions and periodic δ-function kicks with a particular strength on all the sites on one sublattice of a onedimensional system can lead to the formation of multiparticle bound states in three different models 74 .…”

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

“…Although isolated interacting Floquet systems are generally expected to heat up to infinite temperature at infinite time [5][6][7][8][9]80], the physics of such systems at experimentally-relevant timescales is well-captured by the above effective Hamiltonians; indeed, it was recently argued that typical heating rates at high frequencies are suppressed exponentially [81][82][83][84], and longlived pre-thermal Floquet steady states have been predicted [82,[84][85][86]. In particular, rigorous mathematical proofs [82][83][84] supported by numerical studies [10] showed that the mistake in the dynamics due to the approximative character of the HFE is under control for the large frequencies and the experimentally-relevant times considered.…”