Entanglement dynamics after quantum quenches in generic integrable systems
Vincenzo Alba, Pasquale Calabrese
SciPost Phys. 4, 017 (2018) · published 27 March 2018
- doi: 10.21468/SciPostPhys.4.3.017
- Submissions/Reports
Abstract
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhys.4.3.017
TI - Entanglement dynamics after quantum quenches in generic integrable systems
PY - 2018/03/27
UR - https://www.scipost.org/SciPostPhys.4.3.017
JF - SciPost Physics
JA - SciPost Phys.
VL - 4
IS - 3
SP - 017
A1 - Alba, Vincenzo
AU - Calabrese, Pasquale
AB - The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.
ER -
@Article{10.21468/SciPostPhys.4.3.017,
title={{Entanglement dynamics after quantum quenches in generic integrable systems}},
author={Vincenzo Alba and Pasquale Calabrese},
journal={SciPost Phys.},
volume={4},
pages={017},
year={2018},
publisher={SciPost},
doi={10.21468/SciPostPhys.4.3.017},
url={https://scipost.org/10.21468/SciPostPhys.4.3.017},
}
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See all Organizations.- FP7 People: Marie-Curie Actions (FP7 People) (through Organization: European Commission [EC])