Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains

TL;DR

This paper investigates the level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings, revealing unexpected non-Wigner distributions despite the models being nonintegrable, challenging prior assumptions.

Contribution

It demonstrates that nonintegrable XXZ chains with next-nearest-neighbor couplings exhibit non-Wigner level-spacing distributions, contrary to typical expectations.

Findings

Integrable XXZ chains follow Poisson distribution.

Next-nearest-neighbor coupled chains show non-Wigner distributions.

Results challenge the standard link between nonintegrability and Wigner distributions.

Abstract

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