Characterization of quantum chaos by two-point correlation functions

Hrant Gharibyan, Masanori Hanada, Brian Swingle, and Masaki Tezuka
Phys. Rev. E 102, 022213 – Published 25 August 2020
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Abstract

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

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  • Received 7 April 2019
  • Accepted 22 July 2020

DOI:https://doi.org/10.1103/PhysRevE.102.022213

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Hrant Gharibyan1,2, Masanori Hanada3,4,5, Brian Swingle6, and Masaki Tezuka7

  • 1Institute for Quantum Information and Matter, Caltech, 1200 E California Blvd, Pasadena California 91125, USA
  • 2Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
  • 3Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom
  • 4School of Physics and Astronomy, and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • 5Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
  • 6Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 7Department of Physics, Kyoto University, Kyoto 606-8502, Japan

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Issue

Vol. 102, Iss. 2 — August 2020

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