# Weak integrability breaking and level spacing distribution

### Submission summary

 As Contributors: Gabor Takacs Arxiv Link: https://arxiv.org/abs/2103.06308v2 (pdf) Date submitted: 2021-03-23 08:50 Submitted by: Takacs, Gabor Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Statistical and Soft Matter Physics Approaches: Theoretical, Computational

### 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 of the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent cross-over between integrable and chaotic statistics is markedly different between weak and strong breaking of integrability, supporting the claim that perturbations by generalised currents only break integrability at higher order. In addition, for the massless case we find that the critical coupling as a function of the volume $L$ scales with a $1/L^{2}$ law for weak breaking as opposed to the previously found $1/L^{3}$ law for the strong case.

###### Current status:
Editor-in-charge assigned