Evolution of Entanglement Spectra under Generic Quantum Dynamics

Po Yao Chang, Xiao Chen, Sarang Gopalakrishnan, J. H. Pixley

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Article number190602
JournalPhysical review letters
Volume123
Issue number19
DOIs
StatePublished - Nov 6 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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