Universal entanglement spectra in random quantum circuits

ORAL

Abstract

We will discuss the time evolution of the entanglement spectra in a spin-1/2 chain
under random unitary dynamics. We find that the reduced density matrix develops
level repulsion on an O(1) time scale while the bandwidth of the entanglement
spectrum is rapidly changing, well before the subsystem has fully thermalized. In
this locally thermal regime, random matrix theory describes the correlations
between nearby entanglement energy levels but fails to capture global level
correlations in the entanglement spectral form factor or the entanglement density of
states. We find this behavior is universal and holds for a multitude of other quantum
circuits. We will provide a heuristic explanation of our results.

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Presenters

  • Po-Yao Chang

    National Tsing Hua University

Authors

  • Po-Yao Chang

    National Tsing Hua University

  • Xiao Chen

    Kavli Institute for Theoretical Physics, University of California at Santa Barbara, University of California, Santa Barbara, Kavli Institute of Theoretical Physics

  • Sarang Gopalakrishnan

    CUNY College of Staten Island, and CUNY Graduate Center, Physics, CUNY College of Staten Island, Physics and Astronomy, CSI and GC, CUNY, CUNY College of Staten Island; The Graduate Center, CUNY, Department of Physics and Astronomy, CUNY College of Staten Island, Physics, CUNY, College of Staten Island, City University of New York, Physics, The Graduate Center, CUNY

  • Jed Pixley

    Rutgers University, Department of Physics and Astronomy, Rutgers University, Rutgers University, New Brunswick, Department of Physics, Rutgers University, Center for Materials Theory, Rutgers University