• Letter

Scrambling and Lyapunov exponent in spatially extended systems

Anna Keselman, Laimei Nie, and Erez Berg
Phys. Rev. B 103, L121111 – Published 16 March 2021
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Abstract

Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit, the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.

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  • Received 9 October 2020
  • Revised 15 February 2021
  • Accepted 16 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L121111

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Anna Keselman1,2, Laimei Nie3,4, and Erez Berg5

  • 1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
  • 2Microsoft Station Q, Santa Barbara, California 93106-6105, USA
  • 3Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
  • 4Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 5Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

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Issue

Vol. 103, Iss. 12 — 15 March 2021

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