Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

TL;DR

This paper investigates how the level statistics of finite XXZ spin chains with discrete symmetries depend on NNN coupling and anisotropy, revealing the interplay of quantum chaos, integrability, and finite-size effects.

Contribution

It provides a detailed analysis of level statistics in XXZ chains considering discrete symmetries, highlighting the impact of finite-size effects and symmetry mixing on spectral behavior.

Findings

Wigner distribution confirms non-integrability in certain regimes

Finite-size effects cause deviations from Wigner behavior in some cases

Discrete symmetries significantly influence spectral statistics

Abstract

Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (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 non-integrability and Wigner behavior in the spectrum. We also show that non-Wigner behavior appears due to mixed symmetries and finite-size effects in some nonintegrable cases.