Critical Properties of the Many-Body Localization Transition
By V. Khemani, S. Lim, D. Sheng, D. Huse. 2016
224 citations recorded by the source corpus.
The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition which lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of this transition at finite sizes in one dimension. We find that the entanglement entropy of small subsystems looks strongly subthermal in the quantum critical regime, which indicates that it varies discontinuously across the transition as the system-size is taken to infinity, even though many other aspects of the transition look continuous. We also study the variance of the half-chain entanglement entropy which shows a peak near the transition, and find substantial variation in the entropy across eigenstates of the same sample. Further, the sample-to-sample variations in this quantity are strongly growing, and larger than the intra-sample variations. We posit that these results are consistent with a picture in which the transition to the thermal phase is driven by an eigenstate-dependent sparse resonant "backbone" of long-range entanglement, which just barely gains enough strength to thermalize the system on the thermal side of the transition as the system size is taken to infinity. This discontinuity in a global quantity --- the presence of a fully functional bath --- in turn implies a discontinuity even for local properties. We discuss how this picture compares with existing renormalization group treatments of the transition.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/91411b4ecf6bc3b337ca2e50990e826f16c1237f
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Citations in the corpus
- Many-body localization: An introduction and selected topics (2017, unknown): “First in the ergodic regime, the RDM spectrum is very well described by the Marˇcenko–Pastur (MP) distribution, which characterizes the eigenvalues density of a random Wishart matrix [146], as shown in Refs.”
- Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “When the disorder is increased, fluctuations of ergodicity indicators (at least in finite systems) may become anomalous, which has been observed in fluctuations of the entanglement entropy [45, 50–53] and in distributions of other observables [66, 113–116].”
- The ergodic side of the many‐body localization transition (2016, background): “The probability distribution of ∂ S̄A/∂L A close to the MBL transition becomes strongly bimodal even for single disorder realizations [104], although the inter-sample variance is observed to be smaller than the sample-to-sample variance [104, 105].”
- Quantum Entanglement in Neural Network States (2017, unknown): “The Page entropy provides an estimate for entanglement in extended thermal states [90] and has been widely used in the context of quantum chaos [91], blackhole information [92, 93], and many-body localization [94, 95].”
- Avalanches and many-body resonances in many-body localized systems (2021, background): “response of MBL systems [44] and theories of finite-size crossovers between MBL and thermalizing systems [30, 31, 56, 58, 61].”