Physics
Disordered interacting quantum many-body systems can become hopelessly localized. This so-called many-body localization has been studied in one-dimensional systems. In two dimensions, experiments indicate that the localization persists, but because it is difficult to tell the difference between no thermalization and slow thermalization, more theoretical work is needed. Relying on an approximate numerical method, Wahl et al. undertook large-scale simulations of a two-dimensional lattice of bosonic atoms in the presence of interactions and disorder. At intermediate disorder strengths, the on-site entanglement entropies exhibited a bimodal distribution, indicating a coexistence of localized and thermalized states; as disorder was increased, localized states took over. The authors were able to extract a critical disorder strength and set a benchmark for future experiments.
Nat. Phys. 10.1038/s41567-018-0339-x (2018).
Physics
Disordered interacting quantum many-body systems can become hopelessly localized. This so-called many-body localization has been studied in one-dimensional systems. In two dimensions, experiments indicate that the localization persists, but because it is difficult to tell the difference between no thermalization and slow thermalization, more theoretical work is needed. Relying on an approximate numerical method, Wahl et al. undertook large-scale simulations of a two-dimensional lattice of bosonic atoms in the presence of interactions and disorder. At intermediate disorder strengths, the on-site entanglement entropies exhibited a bimodal distribution, indicating a coexistence of localized and thermalized states; as disorder was increased, localized states took over. The authors were able to extract a critical disorder strength and set a benchmark for future experiments.
Nat. Phys. 10.1038/s41567-018-0339-x (2018).
Many-body localization of a disorder interacting boson system in one dimension is studied numerically at the filling factor being one-half, in terms of level statistics, local compressibility, correlation function and entanglement entropies. The von Neumann entanglement entropy is decoupled into a particle number entropy and a configuration entropy. An anomalous volume-law behavior is found for the configuration entanglement entropy to confirm a recent experimental observation [A. Lukin, M. Rispoli, R. Schittko, et al., Science 364, 256 (2019)] for sufficient strong disorder, while the particle number entropy fulfills an area-law corresponding to the total entropy for disordered spin chain. The localization length are extracted from a two-body correlation function for many-body localization states and corresponding time-evolutions states as well. A phase diagrams is established with consisting of an ergodic thermalized region and a many-body-localization region in a parameter space of the disorder strength and the energy density. Two regions are separated by a many-body mobility edge deducted from the standard deviation of the particle-number entanglement entropy, which appears consistent with that based on the localization length. Slow dynamics characterized by a logarithmic time-dependence is explicitly shown for both the particle number entropy and the configuration entropy in an intermediate regime of their time-evolutions, which does not show up in the Anderson localization case, i.e. non-interacting disorder 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.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies have left no doubt about the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered clean component plays the role of a small quantum bath of adjustable size that is collisionally coupled to the dirty component. Our experiments provide evidence that MBL is remarkably stable in 2D and can even survive in the presence of a small bath for our observed long timescales. A too large bath, however, ultimately leads to the destruction of MBL.
Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition, a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this Letter, we explore two entanglement properties that are promising for the study of the many-body localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We, thereby, give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al., Phys. Rev. B 88, 014206 (2013).
Disordered quantum many-body systems pose one of the central challenges in condensed matter physics and quantum information science, as their dynamics are generally intractable for classical computation. Many-body localization (MBL), hypothesized to evade thermalization indefinitely under strong disorder, exemplifies this difficulty. Here, we study the stability of MBL in two dimensions using ultracold atoms in optical lattices with variable system sizes up to 24×24 sites, well beyond the classically simulable regime. Using the imbalance as a probe, we trace the long-time dynamics under two distinctive disorder potentials: quasiperiodic and random disorder. For random disorder, the MBL crossover point shifts to higher disorder strength with increasing system size, consistent with the avalanche scenario. In contrast, with quasiperiodic disorder, we observe no clear system size dependence, suggesting possible stability of MBL in two dimensions.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered ''clean'' component plays the role of a bath of adjustable size that is collisionally coupled to the ''dirty'' component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.