期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2016.0428
关键词
thermalization; many-body localization; eigenstate thermalization hypothesis; non-ergodic delocalized phase; central spin model; thermal inclusions
资金
- Fundacao para a Ciencia e a Tecnologia (Portugal) [SFRH/BD/84875/2012]
- Perimeter Institute for Theoretical Physics
- Industry Canada
- Province of Ontario through the Ministry of Research Innovation
- Sloan Foundation through a Sloan Research Fellowship
- NSF [PHY-1520535]
- Fundação para a Ciência e a Tecnologia [SFRH/BD/84875/2012] Funding Source: FCT
Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N >> 1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale J(c)(N)similar to 1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either 'on' (strongly entangled) or 'off' (weakly entangled) in eigenstates. The clusters of 'on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite.
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