Operator front broadening in chaotic and integrable quantum chains

Javier Lopez-Piqueres, Brayden Ware, Sarang Gopalakrishnan, and Romain Vasseur
Phys. Rev. B 104, 104307 – Published 14 September 2021

Abstract

Operator spreading under unitary time evolution has attracted a lot of attention recently as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOCs) do distinguish interacting from noninteracting systems, it has remained unclear to what extent they can truly diagnose chaotic vs integrable dynamics in many-body quantum systems. Here, we analyze operator spreading in generic one-dimensional many-body quantum systems using a combination of matrix product operator (MPO) and analytical techniques, focusing on the operator right weight. First, we show that while small bond dimension MPOs allow one to capture the exponentially decaying tail of the operator front, in agreement with earlier results, they lead to significant quantitative and qualitative errors for the actual front—defined by the maximum of the right weight. We find that while the operator front broadens diffusively in both integrable and chaotic interacting spin chains, the precise shape and scaling of the height of the front in integrable systems is anomalous for all accessible times. We interpret these results using a quasiparticle picture. This provides a sharp, although rather subtle, signature of many-body quantum chaos in the operator front.

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  • Received 8 April 2021
  • Revised 31 August 2021
  • Accepted 31 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.104307

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyStatistical Physics & Thermodynamics

Authors & Affiliations

Javier Lopez-Piqueres1, Brayden Ware1, Sarang Gopalakrishnan2,3, and Romain Vasseur1

  • 1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 2Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 3Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314, USA

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Issue

Vol. 104, Iss. 10 — 1 September 2021

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