TY - JOUR
T1 - Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
AU - Gopalakrishnan, Sarang
AU - Huse, David A.
N1 - Funding Information:
The authors are grateful to Vedika Khemani and Vadim Oganesyan for helpful discussions, and to an anonymous referee for suggesting we think about many-body mobility edges. S.G. acknowledges support from NSF Grant No. DMR-1653271. D.A.H. is supported in part by the DARPA DRINQS program.
Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/4/16
Y1 - 2019/4/16
N2 - The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus, to define the phase transition, one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called avalanche instability due to rare thermalizing regions in the MBL phase for systems with quenched randomness in two cases: for short-range interacting systems in more than one spatial dimension and for systems in which the interactions fall off with distance as a power law. We find an unconventional way of scaling these systems so that they do have a type of phase transition. Our arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension (or with sufficiently rapidly decaying power laws) is a transition where entanglement in the eigenstates begins to spread into some typical regions: The transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.
AB - The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus, to define the phase transition, one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called avalanche instability due to rare thermalizing regions in the MBL phase for systems with quenched randomness in two cases: for short-range interacting systems in more than one spatial dimension and for systems in which the interactions fall off with distance as a power law. We find an unconventional way of scaling these systems so that they do have a type of phase transition. Our arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension (or with sufficiently rapidly decaying power laws) is a transition where entanglement in the eigenstates begins to spread into some typical regions: The transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.
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U2 - 10.1103/PhysRevB.99.134305
DO - 10.1103/PhysRevB.99.134305
M3 - Article
AN - SCOPUS:85065146931
SN - 2469-9950
VL - 99
JO - Physical Review B
JF - Physical Review B
IS - 13
M1 - 134305
ER -