Level Statistics of XXZ Spin Chains with Descrete Symmetries: Analysis through Finite-size Effetcs

Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbour (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and the XXZ anisotropy, which should reflect competition among quantum chaos, integrability and finite-size effects. Here discrete symmetries play a central role in our analysis. Evaluating the level-spacing distribution, the spectral rigidity and the number variance, we confirm the correspondence between nonintegrability and Wigner behaviour in the spectrum. We also show that non-Wigner behavior appears due to mixed symmetries and finite-size effects in some nonintegrable cases.