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Distinguishing localization from chaos: challenges in finite-size systems
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We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [\v{S}untajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.
Forward citations
Cited by 2 Pith papers
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Time dynamics with matrix product states: Many-body localization transition of large systems revisited
TDVP time evolution with insufficient bond dimension spuriously overestimates delocalization and entanglement in the MBL crossover, and correcting this lowers the estimated critical disorder to Wc = 4.2 ± 0.3.
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Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
Two-dimensional many-body-localized systems with an on-site abelian symmetry are shown to carry a topological index in the (generalized) third cohomology group of the symmetry group, robust to local perturbations.
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