Thouless energy across the many-body localization transition in Floquet systems

Sonner M, Serbyn M, Papić Z, Abanin DA. 2021. Thouless energy across the many-body localization transition in Floquet systems. Physical Review B. 104(8), L081112.


Journal Article | Published | English
Author
Sonner, Michael; Serbyn, MaksymIST Austria ; Papić, Zlatko; Abanin, Dmitry A.
Department
Abstract
The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate and compare the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g., typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, Thouless energy decreases slowly with the system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting and yields insights into the MBL transition in Floquet systems.
Publishing Year
Date Published
2021-08-15
Journal Title
Physical Review B
Acknowledgement
We thank S. Garratt for useful comments on the manuscript. This work was supported by the Swiss National Science Foundation (M. Sonner and D.A.A.) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (M. Serbyn, Grant Agreement No. 850899, and D.A.A., Grant Agreement No. 864597). Z.P. acknowledges support from EPSRC Grant No. EP/R020612/1 and from Leverhulme Trust Research Leadership Award No. RL-2019-015. The computations were performed on the Baobab cluster of the University of Geneva.
Volume
104
Issue
8
Article Number
L081112
ISSN
eISSN
IST-REx-ID

Cite this

Sonner M, Serbyn M, Papić Z, Abanin DA. Thouless energy across the many-body localization transition in Floquet systems. Physical Review B. 2021;104(8). doi:10.1103/PhysRevB.104.L081112
Sonner, M., Serbyn, M., Papić, Z., & Abanin, D. A. (2021). Thouless energy across the many-body localization transition in Floquet systems. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.104.L081112
Sonner, Michael, Maksym Serbyn, Zlatko Papić, and Dmitry A. Abanin. “Thouless Energy across the Many-Body Localization Transition in Floquet Systems.” Physical Review B. American Physical Society, 2021. https://doi.org/10.1103/PhysRevB.104.L081112.
M. Sonner, M. Serbyn, Z. Papić, and D. A. Abanin, “Thouless energy across the many-body localization transition in Floquet systems,” Physical Review B, vol. 104, no. 8. American Physical Society, 2021.
Sonner M, Serbyn M, Papić Z, Abanin DA. 2021. Thouless energy across the many-body localization transition in Floquet systems. Physical Review B. 104(8), L081112.
Sonner, Michael, et al. “Thouless Energy across the Many-Body Localization Transition in Floquet Systems.” Physical Review B, vol. 104, no. 8, L081112, American Physical Society, 2021, doi:10.1103/PhysRevB.104.L081112.
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