Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XXZ</mml:mi></mml:math>spin chains

Abstract

The level-spacing distributions of $\mathrm{XXZ}$ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable $\mathrm{XXZ}$ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearest-neighbor coupled $\mathrm{XXZ}$ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.