Distinguishing localization from chaos: Challenges in finite-size systems

By D. Abanin, J. Bardarson, Giuseppe De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, Frank Pollmann, Andrew C. Potter, Maksym Serbyn, Romain Vasseur. 2019

243 citations recorded by the source corpus.

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 [Suntajs 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/150acd8eddb3cf7a66b5978d13acec1d41c1dca0

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Hilbert Space Fragmentation and Commutant Algebras (2021, background): “Second are Many-Body Localized systems, where strong disorder or quasiperidocity results in the existence of emergent integrals of motion that leads to localized eigenstates throughout the spectrum, although its stability for large system sizes in more than one dimension is a subject of much debate ”
Finite-temperature transport in one-dimensional quantum lattice models (2020, background): “In the discussion of nonintegrable models, we exclude systems with disorder (Abanin et al., 2019a; Altman and Vosk, 2015; Gopalakrishnan and Parameswaran, 2019; Luitz and Lev, 2017; Nandkishore and Huse, 2015).”
Avalanches and many-body resonances in many-body localized systems (2021, background): “We also note that recently there have been a number of papers expressing various levels of skepticism about the stability of the MBL phase in the limits of large systems and very long times [47–53], and a number of challenges to those conclusions [54–58].”
Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “The existence of such stable emergent integrability is however still being debated (51, 52, 53, 54, 55, 56).”