Evolution of Entanglement Spectra under Generic Quantum Dynamics

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

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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
Issue number19
StatePublished - Nov 6 2019

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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