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The many-body localised (MBL) to thermal crossover observed in exactdiagonalisation studies remains poorly understood as the accessiblesystem sizes are too small to be in an asymptotic scaling regime.We develop a model of the crossover in short 1D chains in which theMBL phase is destabilised by the formation of many-body resonances.The model reproduces several properties of the numerically observedcrossover, including an apparent correlation length exponent \nu=1 ν = 1 ,exponential growth of the Thouless time with disorder strength, lineardrift of the critical disorder strength with system size, scale-freeresonances, apparent 1/\omega 1 / ω dependence of disorder-averaged spectral functions, and sub-thermalentanglement entropy of small subsystems.In the crossover, resonances induced by a local perturbation are rareat numerically accessible system sizes L L which are smaller than a \lambda λ .For L \gg \sqrt{\lambda} L ≫ λ (in lattice units), resonances typically overlap, and this model doesnot describe the asymptotic transition.The model further reproduces controversial numerical observationswhich Refs. claimed to be inconsistent with MBL. We thus argue that thenumerics to date is consistent with a MBL phase in the thermodynamiclimit.
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Many-Body Resonances in the Avalanche Instability of Many-Body Localization
Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called “avalanche,” where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.
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- Award ID(s):
- 2120757
- PAR ID:
- 10505917
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Letters
- Volume:
- 130
- Issue:
- 25
- ISSN:
- 0031-9007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevLett.130.250405
