TY - JOUR
T1 - Thermal inclusions
T2 - How one spin can destroy a many-body localized phase
AU - Ponte, Pedro
AU - Laumann, C. R.
AU - Huse, David A.
AU - Chandran, A.
N1 - Funding Information:
Data accessibility. The code to generate the data reported here is available at https://bitbucket.org/ppontem/ centralspinmbl. Authors’ contributions. P.P. carried out numerical simulations and data analysis. All authors contributed to the writing of the manuscript. Competing interests. The authors declare that they have no competing interests. Funding. P.P. acknowledges financial support from Fundação para a Ciência e a Tecnologia (Portugal) through grant SFRH/BD/84875/2012 and the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. C.R.L. acknowledges support from the Sloan Foundation through a Sloan Research Fellowship and the NSF through grant PHY-1520535. Acknowledgements. We thank Wojciech de Roeck, Sarang Gopalakrishnan, Francois Huveneers and Vedika Khemani for helpful discussions.
Publisher Copyright:
© 2017 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2017/12/13
Y1 - 2017/12/13
N2 - 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.
AB - 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.
KW - Central spin model
KW - Eigenstate thermalization hypothesis
KW - Many-body localization
KW - Non-ergodic delocalized phase
KW - Thermal inclusions
KW - Thermalization
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U2 - 10.1098/rsta.2016.0428
DO - 10.1098/rsta.2016.0428
M3 - Article
C2 - 29084891
AN - SCOPUS:85032580466
SN - 0962-8428
VL - 375
JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
IS - 2108
M1 - 20160428
ER -