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arXiv:2108.04834 · Physical review. B./Physical review. B

Many-body localization with quasiperiodic driving

David M. Long, Philip J. D. Crowley, Anushya Chandran

Published Apr 19, 2022• 29 citations
arXivHTMLPDF

Abstract

Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\ensuremath{\ge}3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\ensuremath{\ge}3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.

DOI
10.1103/physrevb.105.144204

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Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by DDD incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for D=2D=2D=2, but not for D\ensuremath≥3D\ensuremath{\ge}3D\ensuremath≥3. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For D\ensuremath≥3D\ensuremath{\ge}3D\ensuremath≥3, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.
Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.
Despite the exponentially large amount of information required in the quantum description of many-body systems, finite size numerical simulations have paved the way for recent progress in the understanding of quantum phases of matter both in and out-of-equilibrium. \n \nIn this spirit, using exact diagonalization for a small number of spins ~ 20, first, we investigate the fate of both ergodic quantum many-body systems that thermalize at long times and systems with quenched disorder that exhibit many-body localization (MBL) and fail to thermalize (due to an extensive set of local conserved degrees of freedom) under periodic driving. Ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local driving, in which the time dependence of the Hamiltonian is restricted to a few contiguous degrees of freedom, and global driving. On the other hand, MBL systems remain localized at finite energy density for local driving, while in the case of global driving these systems can either heat up to infinite temperature or remain localized depending on the parameters of the drive. Underlying the latter is the emergence of an effective time independent MBL Hamiltonian describing the long time dynamics of the system. These numerical predictions have recently been verified experimentally in a one dimensional quasi-disordered optical lattice of interacting fermions wherein unitary time evolution can be experimentally probed. \n \nSubsequently, we study the stability of MBL systems with respect to another perturbation, in this case by thermal inclusions, which remains poorly understood. We consider a simple model to address this question: a two level system interacting with 𝑁 localized bits subject to random fields. In the large 𝑁 limit, the localized bits are thermalized for any nonzero ratio of interactions to disorder strength. Moreover, at finite 𝑁, in the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either "on" (strongly entangled) or "off" (weakly entangled) in eigenstates. The clusters of "on" bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogenous discontinuous transition out of the localized phase in single site observables. These results also imply the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions 𝑑 that are high but finite. \n \nThe second part of this thesis is motivated by the recent breakthroughs of artificial intelligence in domains such as computer vision involving highly dimensional data of complexity not unlike the one found in the description of many-body systems. Using Monte Carlo simulations to generate synthetic data, we find that kernel methods, a class of machine learning algorithms, can learn the mathematical \nform of physical discriminators associated with phase transitions, such as order parameters and Hamiltonian constraints, for a set of two dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. \n \nOur work shows that the combination of numerical simulations with the ability of machine learning algorithms for automatic feature detection hold promise to become standard tools in the exploration and characterization of different phases of matter in condensed matter and other many-body systems.
We investigate the fate of a many-body localized phase in a non-Hermitian quasiperiodic model of hardcore bosons subjected to periodic driving. While in general, the many-body localized system is known to thermalize with increasing driving period due to Floquet heating, in this case, we demonstrate that the initially localized system first delocalizes and then localizes again, resulting in a re-entrant many-body localization (MBL) transition as a function of the driving period. Strikingly, further increase in the driving period results in a series of localization-delocalization transitions leaving behind traces of extended regimes (islands) in between MBL phases. Furthermore, non-Hermiticity renders the extended islands boundary-sensitive, resulting in a Floquet many-body skin effect under open boundaries. We present numerical evidence from spectral and dynamic studies, confirming these findings. Our study opens new pathways for understanding the interplay between non-Hermiticity and quasiperiodicity in driven systems.
Many-body localized (MBL) systems are known to thermalize in periodically driven systems. In this work, we demonstrate that under proper driving protocol, this thermalization this thermalization can be resisted such that the MBL phase turns into a non-ergodic extended phase, known as the many-body critical (MBC) phase. Considering a kicked quasiperiodic Ising chain, we show that while at high-frequency driving the ergodic, MBL, and the MBC phases coexist, at moderate driving frequencies the MBL phase is completely suppressed and the MBC phase proliferates in the parameter space. Using quasienergy statistics, Floquet eigenstates, autocorrelation dynamics, and entanglement growth, we characterize the emergent phases and identify non-monotonic signatures revealing richness of the nonergodic phases. Our results establish Floquet driving as a powerful route to stabilizing nonergodic extended many-body phases beyond the conventional Floquet-MBL paradigm.
The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension d>1d>1d>1, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension d>1d>1d>1. We argue that (i) the MBL phase is stable against ``avalanches'' at strong enough quasiperiodic modulations for d=2d=2d=2, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d\ensuremath{\ge}3$.
Abstract There are exceptions to the general observation that interacting quantum-many body systems thermalize. The most prominent case is many-body localization (MBL) where interactions drive localization in disordered lattice systems. In such systems, the eigenstate thermalization (ETH) hypothesis breaks down and the system remains in a non-thermal state. The existence of MBL in two-dimensional systems and the conditions on required disorder properties are still debated. Here, we study a two-dimensional fermionic quantum many-body system in Moiré-type quasiperiodic disorder and find a novel two-step transition to a MBL state. The intermediate state shows anisotropic transport induced by partial localization. Our work paves the way for the study of the numerous intriguing phenomena observed in Moiré lattice materials and our observations ask for further studies on localization in more complex Moiré structures.