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arXiv · 1811.00029

Evolution of entanglement spectra under generic quantum dynamics

Po-Yao Chang·Xiao Chen·Sarang Gopalakrishnan·J. H. Pixley
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Abstract

We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct timescales. First, on an o(1) timescale, independent of system or subsystem size and the details of the dynamics, the entanglement spectrum develops nearest-neighbor level repulsion. The second timescale sets in when the light-cone has traversed the subsystem. Between these two times, the density of states of the reduced density matrix takes a universal, scale-free 1/f form; thus, random-matrix theory captures the local statistics of the entanglement spectrum but not its global structure. The third time scale is that on which the entanglement saturates; this occurs well after the light-cone traverses the subsystem. Between the second and third times, the entanglement spectrum compresses to its thermal Marchenko-Pastur form. These features hold for chaotic Hamiltonian and Floquet dynamics as well as a range of quantum circuit models.

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Po-Yao Chang, Xiao Chen, Sarang Gopalakrishnan, J. H. Pixley. 2019-08-07. Evolution of entanglement spectra under generic quantum dynamics. https://doi.org/10.1103/physrevlett.123.190602

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