Hydrodynamics of quantum entropies in Ising chains with linear dissipation
- 26 January 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (7), 074002
- https://doi.org/10.1088/1751-8121/ac48ec
Abstract
We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities—such as the von Neumann entropy, the Rényi entropies, and the associated mutual information—admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.Keywords
Funding Information
- Deutsche Forschungsgemeinschaft (435696605)
- German Scholars Organization e.V.
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