Machine learning many-body localization: Search for the elusive nonergodic metal

Eyal Bairey, Gil Refael, Evert van Nieuwenburg

Mattias Jönsson

Wei Zhang, Lei Wang, Ziqiang Wang

Yi‐Ting Hsu, Xiao Li, Dong-Ling Deng +1 more

The breaking of ergodicity in isolated quantum systems with a single-particle mobility edge is an intriguing subject that has not yet been fully understood. In particular, whether a nonergodic but metallic phase exists or not in the presence of a one-dimensional quasiperiodic potential is currently under active debate. In this Letter, we develop a neural-network-based approach to investigate the existence of this nonergodic metallic phase in a prototype model using many-body entanglement spectra as the sole diagnostic. We find that such a method identifies with high confidence the existence of a nonergodic metallic phase in the midspectrum at an intermediate quasiperiodic potential strength. Our neural-network-based approach shows how supervised machine learning can be applied not only in locating phase boundaries but also in providing a way to definitively examine the existence or not of a novel phase.

Lili Ye, Ying‐Cheng Lai

Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods relied largely on theoretical model of the target quantum system, but invertible model approximations and inaccuracies can lead to control failures. We develop a model-free and deep reinforcement-learning (DRL) framework for quantum nonergodicity control. It is a machine-learning method with the unique focus on balancing exploration and exploitation strategies to maximize the cumulative rewards so as to preserve the initial memory in the time-dependent nonergodic metrics over a long stretch of time. We use the paradigmatic one-dimensional tilted Fermi-Hubbard system to demonstrate that the DRL agent can efficiently learn the quantum many-body system solely through the interactions with the environment. The optimal policy obtained by the DRL provides broader control scenarios for managing nonergodicity in the phase diagram as compared to, e.g., the specific protocol for Wannier-Stark localization. The continuous control protocols and observations are experimentally feasible. The model-free nature of DRL and its versatile search space for control functions render promising nonergodicity control in more complex quantum many-body systems.

Samuel T. Savitz, Changnan Peng, Gil Refael

Anderson localization on treelike graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the possibility of nonergodic extended regimes. This behavior has been conjectured to also appear in many-body localization as a ``bad metal'' phase, and constitutes an intermediate possibility between the extremes of ergodic quantum chaos and integrable localization. Despite decades of research, a complete consensus understanding of this model remains elusive. Here we use cages, maximally treelike structures from extremal graph theory; and numerical continuous unitary Wegner flows of the Anderson Hamiltonian to develop an intuitive picture which, after extrapolating to the infinite Bethe lattice, appears to capture ergodic, nonergodic extended, and fully localized behavior.