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/L^{2}1/L2 law for weak breaking as opposed to the 1/L^{3}1/L3 law previously found for the strong case.
Highlights
Mean values of generalised currents in one-dimensional integrable models have attracted considerable interest lately, mainly due to the recent theory of Generalised Hydrodynamics which describes non-equilibrium dynamics at the Euler scale [1,2]
In [7] an algebraic construction was given for the current operators of the integrable spin chains, which led to an alternative rigorous proof of their mean values
[8] it was discovered that these exact results are connected to the so-called long range deformations of integrable spin chains which emerged in the context of the AdS/CFT correspondence [9,10,11]
Summary
Mean values of generalised currents in one-dimensional integrable models have attracted considerable interest lately, mainly due to the recent theory of Generalised Hydrodynamics which describes non-equilibrium dynamics at the Euler scale [1,2] These currents express the continuity relation for conserved charges responsible for integrability, which can be exploited for a hydrodynamic description of the ballistic flow of the quasi-particles. For systems without a spectral gap, the crossover coupling scales as a (negative) power of the volume, with the exponent depending whether the local degrees of freedom are interacting or not [30]; for the case with interactions, the behaviour was determined to be L−3, irrespective of the spatial dimensionality of the system In this short paper we set out to investigate the weak breaking of integrability by exploring the level spacing statistics for the case of the spin-1/2 XXZ spin chain.
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