Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal

Hsu, Yi-Ting; Li, Xiao; Deng, Dong-Ling; Sarma, S. Das

doi:10.1103/physrevlett.121.245701

Cited by 96 publications

(67 citation statements)

References 68 publications

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“…We emphasize that the S phase we report here is naively different from the intermediate phase observed in certain GAA models [18][19][20]61] or in systems with quenched disorder [27][28][29]. In the former case, the manybody intermediate phase may be attributed to the existence of a single-particle mobility edge in the noninteracting limit, while in the latter case rare region Griffiths physics may play a role.…”

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confidence: 79%

Butterfly effect in interacting Aubry-Andre model: Thermalization, slow scrambling, and many-body localization

Hsu

et al. 2019

Phys. Rev. Research

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The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments. arXiv:1902.07199v1 [cond-mat.str-el]

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confidence: 79%

Butterfly effect in interacting Aubry-Andre model: Thermalization, slow scrambling, and many-body localization

Hsu

et al. 2019

Phys. Rev. Research

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“…To further corroborate our analysis, we apply methods from machine learning [57], which has emerged recently as a powerful tool to analyze localization phenomena [58][59][60][61][62][63], to our data obtained using the TDVP. We use two algorithms: a partially supervised approach that has previously been employed in Ref.…”

Section: Machine Learningmentioning

confidence: 99%

Many-body localization and delocalization in large quantum chains

et al. 2018

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We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to L = 100 spins, i.e., much larger than L 20 that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent β which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent βΛ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder Wc that separates the ergodic and many-body localized regimes, compared to the values of Wc in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents β and βΛ increase, with increasing L, for relatively small L but saturate for L 50, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine Wc. arXiv:1807.05051v4 [cond-mat.dis-nn]

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“…(ii) Does the SPIP survive finite interactions to become a many-body intermediate phase (MBIP)? This would suggest the existence of an intermediate phase, where extended and localized many-body states coexist in the energy spectrum [15,16,42,43]. Note that this does not necessarily require the existence of a many-body mobility edge, instead a coexistence of localized and extended many-body states at fixed energy density has been predicted in certain models [43].…”

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confidence: 94%

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge

et al. 2019

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We experimentally study many-body localization (MBL) with ultracold atoms in a weak onedimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.arXiv:1809.04055v3 [cond-mat.quant-gas]

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Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal

Cited by 96 publications

References 68 publications

Butterfly effect in interacting Aubry-Andre model: Thermalization, slow scrambling, and many-body localization

Butterfly effect in interacting Aubry-Andre model: Thermalization, slow scrambling, and many-body localization

Many-body localization and delocalization in large quantum chains

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge

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