Thermal inclusions: How one spin can destroy a many-body localized phase

Pedro Ponte, C. R. Laumann, David A. Huse, A. Chandran

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


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) - 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.

Original languageEnglish (US)
Article number20160428
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2108
StatePublished - Dec 13 2017

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


  • Central spin model
  • Eigenstate thermalization hypothesis
  • Many-body localization
  • Non-ergodic delocalized phase
  • Thermal inclusions
  • Thermalization


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