Distinctive response of many-body localized systems to a strong electric field

Abstract

We study systems which are close to or within the many-body localized (MBL) regime and are driven by strong electric field. In the ergodic regime, the disorder extends applicability of the equilibrium linear-response theory to stronger drivings, whereas the response of the MBL systems is very distinctive, revealing currents with damped oscillations. The oscillation frequency is independent of driving and the damping is not due to heating but rather due to dephasing. The details of damping depend on the system's history reflecting nonergodicity of the MBL phase, while the frequency of the oscillations remains a robust hallmark of localization. We show that the distinctive characteristic of the driven MBL phase is also a logarithmic increase of the energy and the polarization with time.

Periodically driving a many-body localized quantum system

“…This result suggests a novel periodically driven regime which would not delocalize for any frequency, as supported by numerical simulations to long times (see supplements [33]). We note that this apparent stability at low frequencies does not contradict previous theoretical studies, which have focused on oscillating linear potentials [13,14,16]. In that case, the system can always delocalize at low enough frequencies because of long-distance Landau-Zener crossings [13,16].…”

“…Particularly, in periodically driven systems exotic phenomena can emerge that are absent in their undriven counterparts. For example, topologically nontrivial band structures can be realized by driving topologically trivial systems [3][4][5][6][7][8][9] and ergodic phases can be created by driving non-ergodic quantum systems [10][11][12][13][14][15][16].In undriven systems, a robust non-ergodic phase can be realized by adding strong disorder to an interacting many-body system, leading to the phenomenon of manybody localization (MBL) [17][18][19][20][21][22][23][24][25]. In an ideal MBL phase, global transport and thermalization are absent, and some memory of the initial conditions persists locally for arbitrarily long times even at finite energy densities [19,20], as underlined in experiments [22][23][24][25].…”

“…Particularly, in periodically driven systems exotic phenomena can emerge that are absent in their undriven counterparts. For example, topologically nontrivial band structures can be realized by driving topologically trivial systems [3][4][5][6][7][8][9] and ergodic phases can be created by driving non-ergodic quantum systems [10][11][12][13][14][15][16].…”

Delocalized carriers in the t−J model with strong charge disorder

“…Most of the inherent properties of MBL systems have been investigated using the generic one-dimensional (1D) disordered models of interacting spinless fermions [21][22][23][24][25][26][27][28][29][30][31]. Emerging characteristic features of MBL systems are: the existence of localized many-body states in the whole energy spectrum that leads to vanishing of d.c. transport at any temperature [32][33][34][35][36][37][38][39], Poisson-like level statistics [40], and the logarithmic growth of the entanglement entropy [5,7,[41][42][43][44][45]. Numerical calculations of dynamical conductivity [34,37,38] and other dynamic properties based on the renormalizationgroup approach [7,35,46,47] indicate that in the vicinity of the transition to MBL state the optical conductivity shows a characteristic linear ω-dependence.…”

Effective realization of random magnetic fields in compounds with large single-ion anisotropy

“…The latter, is an interacting analog of Anderson localization 3 and the properties of a system close to, at, or in such a phase are a focus of many recent theoretical studies. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] On the other hand, experimental studies of such phenomena are surprisingly rare, mainly due to the lack of real world realizations of strong enough disorder. Recently a few studies of cold atoms on optical lattices [22][23][24] and a study of short ion chains 25 were preformed.…”