In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a noninteracting model exhibiting algebraically localized single-particle modes. For this model we find numerically that the algebraically localized phase is stable under driving, meaning that the system remains localized at arbitrary frequencies. We support this result with analytical considerations using simple renormalization group arguments. Second, we inspect the case in which short-range interactions are added. By studying both the eigenstate properties of the Floquet Hamiltonian and the out-of-equilibrium dynamics in the interacting model, we provide evidence that ergodicity is restored at any driving frequencies. In particular, we observe that for the accessible system sizes localization sets in at driving frequency that is comparable with the many-body bandwidth and thus it might be only transient, suggesting that the system might thermalize in the thermodynamic limit.
In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a noninteracting model exhibiting algebraically localized single-particle modes. For this model we find numerically that the algebraically localized phase is stable under driving, meaning that the system remains localized at arbitrary frequencies. We support this result with analytical considerations using simple renormalization group arguments. Second, we inspect the case in which short-range interactions are added. By studying both the eigenstate properties of the Floquet Hamiltonian and the out-of-equilibrium dynamics in the interacting model, we provide evidence that ergodicity is restored at any driving frequencies. In particular, we observe that for the accessible system sizes localization sets in at driving frequency that is comparable with the many-body bandwidth and thus it might be only transient, suggesting that the system might thermalize in the thermodynamic limit.
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 study the stability of localization under periodic driving in Stark many-body systems. We find that localization is stable except near special resonant frequencies, where resonances cause delocalization. We provide approximate analytical arguments and numerical evidence in support of these results. This shows that disorder-free broken ergodicity is stable to driving, opening up the way to studying nonequilibrium driven physics in a different setting. Published by the American Physical Society 2024
When pushed out of equilibrium, generic interacting quantum systems equilibrate locally and are expected to evolve towards a locally thermal description despite their unitary time evolution. Systems in which disorder competes with interactions and transport can violate this expectation by exhibiting many-body localization. The strength of the disorder with respect to the other two parameters drives a transition from a thermalizing system towards a nonthermalizing one. The existence of this transition is well established both in experimental and numerical studies for finite systems. However, the stability of many-body localization in the thermodynamic limit is largely unclear. With increasing system size, a generic disordered system will contain with high probability areas of low disorder variation. If large and frequent enough, those areas constitute ergodic grains which can hybridize and thus compete with localization. While the details of this process are not yet settled, it is conceivable that if such regions appear sufficiently often, they might be powerful enough to restore thermalization. We set out to shed light on this problem by constructing potential landscapes with low disorder regions and numerically investigating their localization behavior in the Heisenberg model. Our findings suggest that many-body localization may be more stable than anticipated in other recent theoretical works.
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.
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.
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.