Level statistics of XXZ spin chains with a random magnetic field

TL;DR

This study investigates how the energy level statistics of a disordered XXZ spin chain vary with system size, anisotropy, and magnetic field, revealing transitions between integrable and nonintegrable behaviors.

Contribution

It provides a detailed numerical analysis of level-spacing distributions in disordered XXZ chains, highlighting the effects of anisotropy and magnetic field strength on quantum chaos signatures.

Findings

Wigner-like level statistics dominate when $ abla e 0$

Poisson-like behavior appears at $ abla=0$ despite nonintegrability

Large magnetic fields induce Poisson-like distributions regardless of anisotropy

Abstract

The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude of the random magnetic field h. In the energy spectrum, quantum integrability competes with nonintegrability derived from the randomness, where the XXZ interaction is modified by the parameter $\Delta$. When $\Delta \ne 0$, the level-spacing distribution mostly shows Wigner-like behavior, while when $\Delta$=0, Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\Delta \ne 0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.