@article{ISI:000469327100005,
 abstract = {Recent work by De Roeck et al. [Phys. Rev. B 95, 155129 (2017)] has
argued that many-body localization is unstable in two and higher
dimensions due to a thermalization avalanche triggered by rare regions
of weak disorder. To examine these arguments, we construct several
models of a finite ergodic bubble coupled to an Anderson insulator of
noninteracting fermions. We first describe the ergodic region using a
Gaussian orthogonal ensemble random matrix and perform an exact
diagonalization study of small systems. The results are in excellent
agreement with a refined theory of the thermalization avalanche that
includes transient finite-size effects, lending strong support to the
avalanche scenario. We then explore the limit of large system sizes by
modeling the ergodic region via a Hubbard model with all-to-all random
hopping: the combined system, consisting of the bubble and the
insulator, can be reduced to an effective Anderson impurity problem. We
find that the spectral function of a local operator in the ergodic
region changes dramatically when coupling to a large number of localized
fermionic states; this occurs even when the localized sites are weakly
coupled to the bubble. In principle, for a given size of the ergodic
region, this may arrest the avalanche. However, this back-action effect
is suppressed and the avalanche can be recovered if the ergodic bubble
is large enough. Thus, the main effect of the back-action is to
renormalize the critical bubble size.},
 article-number = {205149},
 author = {Potirniche, Ionut-Dragos and Banerjee, Sumilan and Altman, Ehud},
 doi = {10.1103/PhysRevB.99.205149},
 eissn = {2469-9969},
 issn = {2469-9950},
 journal = {PHYSICAL REVIEW B},
 month = {MAY 28},
 number = {20},
 title = {Exploration of the stability of many-body localization in d > 1},
 unique-id = {ISI:000469327100005},
 volume = {99},
 year = {2019}
}