Quantum quenches in the many-body localized phase

M. Serbyn, Z. Papić, D. Abanin, Physical Review B - Condensed Matter and Materials Physics 90 (2014).


Journal Article | Published
Author
Serbyn, MaksymIST Austria ; Papić, Zlatko; Abanin, Dmitry A
Abstract
Many-body localized (MBL) systems are characterized by the absence of transport and thermalization and, therefore, cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behavior of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly nonthermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behavior distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached) and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultracold atoms in disordered optical lattices, and the behavior of local observables provides a direct experimental signature of many-body localization.
Publishing Year
Date Published
2014-11-06
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Acknowledgement
Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation. We acknowledge support by NSERC Discovery Grant (D.A.).
Volume
90
Issue
17
IST-REx-ID
980

Cite this

Serbyn M, Papić Z, Abanin D. Quantum quenches in the many-body localized phase. Physical Review B - Condensed Matter and Materials Physics. 2014;90(17). doi:10.1103/PhysRevB.90.174302
Serbyn, M., Papić, Z., & Abanin, D. (2014). Quantum quenches in the many-body localized phase. Physical Review B - Condensed Matter and Materials Physics, 90(17). https://doi.org/10.1103/PhysRevB.90.174302
Serbyn, Maksym, Zlatko Papić, and Dmitry Abanin. “Quantum Quenches in the Many-Body Localized Phase.” Physical Review B - Condensed Matter and Materials Physics 90, no. 17 (2014). https://doi.org/10.1103/PhysRevB.90.174302.
M. Serbyn, Z. Papić, and D. Abanin, “Quantum quenches in the many-body localized phase,” Physical Review B - Condensed Matter and Materials Physics, vol. 90, no. 17, 2014.
Serbyn M, Papić Z, Abanin D. 2014. Quantum quenches in the many-body localized phase. Physical Review B - Condensed Matter and Materials Physics. 90(17).
Serbyn, Maksym, et al. “Quantum Quenches in the Many-Body Localized Phase.” Physical Review B - Condensed Matter and Materials Physics, vol. 90, no. 17, American Physical Society, 2014, doi:10.1103/PhysRevB.90.174302.
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