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 $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.
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- 1 Budapesti Műszaki és Gazdaságtudományi Egyetem / Budapest University of Technology and Economics [BUTE]
- 2 Eötvös Loránd Tudományegyetem / Eötvös Loránd University [ELTE]
- Emberi Eroforrások Minisztériuma (through Organization: Emberi Erőforrások Minisztérium / Ministry of Human Capacities [Emmi])
- Nemzeti Kutatási, Fejlesztési és Innovációs Hivatal / National Research, Development and Innovation Office [NKFIH]