Loschmidt echo in many body localized phases

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


Journal Article | Published
Author
Serbyn, MaksymIST Austria ; Abanin, Dimitry A
Abstract
The Loschmidt echo, defined as the overlap between quantum wave function evolved with different Hamiltonians, quantifies the sensitivity of quantum dynamics to perturbations and is often used as a probe of quantum chaos. In this work we consider the behavior of the Loschmidt echo in the many-body localized phase, which is characterized by emergent local integrals of motion and provides a generic example of nonergodic dynamics. We demonstrate that the fluctuations of the Loschmidt echo decay as a power law in time in the many-body localized phase, in contrast to the exponential decay in few-body ergodic systems. We consider the spin-echo generalization of the Loschmidt echo and argue that the corresponding correlation function saturates to a finite value in localized systems. Slow, power-law decay of fluctuations of such spin-echo-type overlap is related to the operator spreading and is present only in the many-body localized phase, but not in a noninteracting Anderson insulator. While most of the previously considered probes of dephasing dynamics could be understood by approximating physical spin operators with local integrals of motion, the Loschmidt echo and its generalizations crucially depend on the full expansion of the physical operators via local integrals of motion operators, as well as operators which flip local integrals of motion. Hence these probes allow one to get insights into the relation between physical operators and local integrals of motion and access the operator spreading in the many-body localized phase.
Publishing Year
Date Published
2017-07-12
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Acknowledgement
This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. M.S. was supported by Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No. GBMF4307. D.A. also acknowledges support by Swiss National Science Foundation.
Volume
96
Issue
1
IST-REx-ID
445

Cite this

Serbyn M, Abanin D. Loschmidt echo in many body localized phases. Physical Review B - Condensed Matter and Materials Physics. 2017;96(1). doi:10.1103/PhysRevB.96.014202
Serbyn, M., & Abanin, D. (2017). Loschmidt echo in many body localized phases. Physical Review B - Condensed Matter and Materials Physics. American Physical Society. https://doi.org/10.1103/PhysRevB.96.014202
Serbyn, Maksym, and Dimitry Abanin. “Loschmidt Echo in Many Body Localized Phases.” Physical Review B - Condensed Matter and Materials Physics. American Physical Society, 2017. https://doi.org/10.1103/PhysRevB.96.014202.
M. Serbyn and D. Abanin, “Loschmidt echo in many body localized phases,” Physical Review B - Condensed Matter and Materials Physics, vol. 96, no. 1. American Physical Society, 2017.
Serbyn M, Abanin D. 2017. Loschmidt echo in many body localized phases. Physical Review B - Condensed Matter and Materials Physics. 96(1).
Serbyn, Maksym, and Dimitry Abanin. “Loschmidt Echo in Many Body Localized Phases.” Physical Review B - Condensed Matter and Materials Physics, vol. 96, no. 1, American Physical Society, 2017, doi:10.1103/PhysRevB.96.014202.
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