Journal
PHYSICAL REVIEW B
Volume 95, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.95.155129
Keywords
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Funding
- Deutsche Forschungsgesellschaft [RO 4522/1-1]
- project EDNHS of the French National Research Agency (ANR) [ANR-14-CE25-0011]
- CNRS InPhyNiTi Grant (MaBoLo)
- Agence Nationale de la Recherche (ANR) [ANR-14-CE25-0011] Funding Source: Agence Nationale de la Recherche (ANR)
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We propose a theory that describes quantitatively the (in)stability of fully many-body localization (MBL) systems due to ergodic, i.e., delocalized, grains, that can be, for example, due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly-even without relying on the theory of local integrals of motion (LIOM)-the MBL phase in one dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d = 1 and (2) always in d > 1. Finer numerics is required to assess these predictions.
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