Spectrum statistics in the integrable Lieb-Liniger model

Samy Mailoud, Fausto Borgonovi, and Felix M. Izrailev
Phys. Rev. E 104, 034212 – Published 15 September 2021

Abstract

We address the old and widely debated question of the spectrum statistics of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of one-dimensional interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is to reveal the characteristic properties of energy levels in dependence of the model parameters. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. By studying long-range correlations between energy levels, we found strong deviations from the predictions based on the assumption of pseudorandom character of the distribution of energy levels.

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  • Received 3 May 2021
  • Revised 27 July 2021
  • Accepted 5 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034212

©2021 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

Samy Mailoud1, Fausto Borgonovi2,3, and Felix M. Izrailev1,4

  • 1Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
  • 2Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia, Italy
  • 3Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, I-27100 Pavia, Italy
  • 4Department of Physics and Astronomy, Michigan State University, E. Lansing, Michigan 48824-1321, USA

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Issue

Vol. 104, Iss. 3 — September 2021

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