English

Weak integrability breaking and level spacing distribution

Statistical Mechanics 2023-08-23 v4 Chaotic Dynamics

Abstract

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume LL scales with a 1/L21/L^2 law for weak breaking as opposed to the 1/L31/L^3 law previously found for the strong case.

Keywords

Cite

@article{arxiv.2103.06308,
  title  = {Weak integrability breaking and level spacing distribution},
  author = {D. Szász-Schagrin and B. Pozsgay and G. Takács},
  journal= {arXiv preprint arXiv:2103.06308},
  year   = {2023}
}

Comments

15 pages, 12 figures. v2: references added. v3: text thoroughly revised, presentation clarified and improved, main results and conclusions unchanged. v4: typos in the formula of the current fixed, the definition of operator norm corrected

R2 v1 2026-06-23T23:58:34.512Z