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Statistics of the spectral form factor in the self-dual kicked Ising model

Ana Flack, Bruno Bertini, and Tomaž Prosen
Phys. Rev. Research 2, 043403 – Published 22 December 2020

Abstract

We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at long enough times the probability distribution agrees exactly with the prediction of random-matrix theory if one identifies the appropriate ensemble of random matrices. We find that this ensemble is not the circular orthogonal one—composed of symmetric random unitary matrices and associated with time-reversal-invariant evolution operators—but is an ensemble of random matrices on a more restricted symmetric space [depending on the parity of the number of sites this space is either Sp(N)/U(N) or O(2N)/O(N)×O(N)]. Even if the latter ensembles yield the same averaged spectral form factor as the circular orthogonal ensemble, they show substantially enhanced fluctuations. This behavior is due to a recently identified additional antiunitary symmetry of the self-dual kicked Ising model.

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  • Received 15 September 2020
  • Accepted 30 November 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043403

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Ana Flack, Bruno Bertini, and Tomaž Prosen

  • Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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Issue

Vol. 2, Iss. 4 — December - December 2020

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