Level statistics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XXZ</mml:mi></mml:math>spin chains with a random magnetic field

Abstract

The level-spacing distribution of a spin-$\frac{1}{2}$ $\mathrm{XXZ}$ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\ensuremath{\Delta},$ 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 $\mathrm{XXZ}$ interaction is modified by the parameter $\ensuremath{\Delta}.$ When $\ensuremath{\Delta}\ensuremath{\ne}0,$ the level-spacing distribution mostly shows Wigner-like behavior, while when $\ensuremath{\Delta}=0,$ Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\ensuremath{\Delta}\ensuremath{\ne}0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.