From the eigenstate thermalization hypothesis to algebraic relaxation of OTOCs in systems with conserved quantities

Vinitha Balachandran, Giuliano Benenti, Giulio Casati, and Dario Poletti
Phys. Rev. B 104, 104306 – Published 14 September 2021

Abstract

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a means to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propagation of correlations for finite-range-interaction systems. We show that time independence of the Hamiltonian is not necessary as the above conditions (i) and (ii) can occur in time-dependent systems, both periodic or aperiodic. We also remark that our result can be extended to systems with power-law interactions.

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  • Received 14 June 2021
  • Revised 4 August 2021
  • Accepted 26 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.104306

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsAtomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Vinitha Balachandran1, Giuliano Benenti2,3,4, Giulio Casati2,5, and Dario Poletti1,6

  • 1Science, Mathematics, and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
  • 2Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
  • 3Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
  • 4NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
  • 5International Institute of Physics, Federal University of Rio Grande do Norte, Natal, Brazil
  • 6EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore

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Issue

Vol. 104, Iss. 10 — 1 September 2021

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