Thouless energy and multifractality across the many-body localization transition

M. Serbyn, P. Zlatko, D. Abanin, Physical Review B - Condensed Matter and Materials Physics 96 (2017).


Journal Article | Published | English
Author
; ;
Department
Abstract
Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this transition in two different models of disordered spin chains. We show that the behavior of matrix elements can be used to characterize the breakdown of thermalization and to extract the many-body Thouless energy. We find that upon increasing the disorder strength the system enters a critical region around the many-body localization transition. The properties of the system in this region are: (i) the Thouless energy becomes smaller than the level spacing, (ii) the matrix elements show critical dependence on the energy difference, and (iii) the matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. This critical region decreases with the system size, which we interpret as evidence for a diverging correlation length at the many-body localization transition. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values and shed light on the critical behavior near the many-body localization transition.
Publishing Year
Date Published
2017-09-06
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Acknowledgement
We acknowledge useful discussions with V. Kravtsov, T. Grover, and R. Vasseur. M.S. was supported by Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4307. M.S. and D.A. acknowledge hospitality of KITP, where parts of this work were completed (supported in part by the National Science Foundation under Grant No. NSF PHY11-25915)
Volume
96
Issue
10
Article Number
104201
ISSN
IST-REx-ID

Cite this

Serbyn M, Zlatko P, Abanin D. Thouless energy and multifractality across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 2017;96(10). doi:10.1103/PhysRevB.96.104201
Serbyn, M., Zlatko, P., & Abanin, D. (2017). Thouless energy and multifractality across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics, 96(10). https://doi.org/10.1103/PhysRevB.96.104201
Serbyn, Maksym, Papic Zlatko, and Dmitry Abanin. “Thouless Energy and Multifractality across the Many-Body Localization Transition.” Physical Review B - Condensed Matter and Materials Physics 96, no. 10 (2017). https://doi.org/10.1103/PhysRevB.96.104201.
M. Serbyn, P. Zlatko, and D. Abanin, “Thouless energy and multifractality across the many-body localization transition,” Physical Review B - Condensed Matter and Materials Physics, vol. 96, no. 10, 2017.
Serbyn M, Zlatko P, Abanin D. 2017. Thouless energy and multifractality across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 96(10).
Serbyn, Maksym, et al. “Thouless Energy and Multifractality across the Many-Body Localization Transition.” Physical Review B - Condensed Matter and Materials Physics, vol. 96, no. 10, 104201, American Physical Society, 2017, doi:10.1103/PhysRevB.96.104201.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar