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arXiv:1912.09487 · Physical review. B./Physical review. B

Drive-induced many-body localization and coherent destruction of Stark many-body localization

Devendra Singh Bhakuni, Ritu Nehra, Auditya Sharma

Published Jul 13, 2020• 27 citations
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Abstract

We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined dc as well as square-wave ac electric field. First, the condition for the dynamic localization and coherent destruction of Wannier-Stark localization in the noninteracting limit is obtained semiclassically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to ``Stark-MBL'' for sufficiently large field strengths. We find that in the presence of an additional high-frequency ac field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive $(A/\ensuremath{\omega})$ is tuned at the dynamic localization point of the noninteracting limit, or by off-resonant drive. Remarkably, resonant drive with $A/\ensuremath{\omega}$ tuned away from the dynamic localization point leads to a coherent destruction of Stark-MBL. Moreover, a pure (high-frequency) ac field can also give rise to the MBL phase if $A/\ensuremath{\omega}$ is tuned at the dynamic localization point of the zero dc field problem.

DOI
10.1103/physrevb.102.024201

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We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined dc as well as square-wave ac electric field. First, the condition for the dynamic localization and coherent destruction of Wannier-Stark localization in the noninteracting limit is obtained semiclassically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to ``Stark-MBL'' for sufficiently large field strengths. We find that in the presence of an additional high-frequency ac field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive (A/\ensuremathω)(A/\ensuremath{\omega})(A/\ensuremathω) is tuned at the dynamic localization point of the noninteracting limit, or by off-resonant drive. Remarkably, resonant drive with A/\ensuremathωA/\ensuremath{\omega}A/\ensuremathω tuned away from the dynamic localization point leads to a coherent destruction of Stark-MBL. Moreover, a pure (high-frequency) ac field can also give rise to the MBL phase if A/\ensuremathωA/\ensuremath{\omega}A/\ensuremathω is tuned at the dynamic localization point of the zero dc field problem.
We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to Stark many-body localization, for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive (A/ωA/\omegaA/ω) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with A/ωA/\omegaA/ω tuned away from the dynamical localization point leads to a \emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if A/ωA/\omegaA/ω is tuned at the dynamical localization point of the zero dc field problem.
We study the fate of many-body localization (MBL) in the presence of long-range hopping ($\ensuremath{\sim}1/{r}^{\ensuremath{\sigma}}$) in a system subjected to an electric field (static and time periodic) along with a slowly varying aperiodic potential. We show that the MBL in the static electric field model is robust against arbitrary long-range hopping, in sharp contrast to other disordered models, where MBL is killed by sufficiently long range hopping. Next, we show that the drive-induced phenomena associated with an ac square wave electric field are also robust against long-range hopping. Specifically, we obtain drive-induced MBL, where a high-frequency drive can convert the ergodic phase into the MBL phase. Remarkably, we find that a coherent destruction of MBL is also possible with the aid of a resonant drive. Thus in both the static and time-periodic square wave electric field models, the qualitative properties of the system are independent of whether the hopping is short range or long range.
Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hard-core bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent destruction of tunneling for engineering long-lived Floquet phases.
In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.
Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight into the properties of Stark MBL and to discover unique entanglement characteristics specific to this phenomenon. The phase diagram analysis reveals different behavior with varying interaction strengths. Furthermore, we highlight the influence of domain wall structures on the breakdown of the entanglement entropy of the system. Moreover, the investigation of Out-of-Time-Ordered Correlator (OTOC) behavior demonstrates distinct responses to interactions based on domain wall configurations. Our findings contribute to a better understanding of Stark MBL and offer valuable insights into the entanglement properties of systems subjected to Stark potentials.
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 $\ensuremath{\tau}$ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down ($\ensuremath{\tau}$ shoots up) by orders of magnitude as the ratio of the drive frequency $\ensuremath{\omega}$ and amplitude h0{h}_{0}h0​ tends to certain specific values (the freezing condition). If $\ensuremath{\omega}$ is increased while maintaining the ratio ${h}_{0}/\ensuremath{\omega}$ at a fixed freezing value, then $\ensuremath{\tau}$ diverges exponentially with $\ensuremath{\omega}.$ The results can be easily extended for a larger family of disordered fermionic and bosonic systems.