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arXiv:2008.13713 · Physical review. B./Physical review. B

Stability of electric field driven many-body localization in an interacting long-range hopping model

Devendra Singh Bhakuni, Auditya Sharma

Published Aug 17, 2020• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.085133

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We study the fate of many-body localization (MBL) in the presence of long-range hopping (\ensuremath∼1/r\ensuremathσ\ensuremath{\sim}1/{r}^{\ensuremath{\sigma}}\ensuremath∼1/r\ensuremathσ) 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.
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.
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 many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions and long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single-particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping [$t(r)\ensuremath{\sim}{t}_{0}/{r}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<2$], there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with $1<\ensuremath{\alpha}<2$ delocalizes the system partially, with almost all the states extended for $\ensuremath{\alpha}\ensuremath{\le}1$. Even in a system which has single-particle mobility edges in the noninteracting limit, turning on long-range interactions does not cause delocalization.
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.
We investigate the role of a quasiperiodically driven electric field in a disordered fermionic chain. In the clean noninteracting case, we show the emergence of dynamical localization---a phenomenon previously known to exist only for a perfect periodic drive. In contrast, in the presence of disorder, where a high-frequency periodic drive preserves Anderson localization, we show that the quasiperiodic drive destroys it and leads to slow relaxation. Considering the role of interactions, we uncover the phenomenon of quasiperiodic driving-induced logarithmic relaxation, where a suitably tuned drive (corresponding to dynamical localization in the clean, noninteracting limit) slows down the dynamics even when the disorder is small enough for the system to be in the ergodic phase. This is in sharp contrast to the fast relaxation seen in the undriven model, as well as the absence of thermalization (drive-induced many-body localization) exhibited by a high-frequency periodic drive.
We study systems that are close to or within the many-body localized (MBL) regime and are driven by a strong electric field. In the ergodic regime, the disorder extends the 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 the nonergodicity of the MBL phase, while the frequency of the oscillations remains a robust hallmark of localization. Our results suggest that another distinctive characteristic of the driven MBL phase is also a logarithmic increase of the energy and the polarization with time.