Level statistics of $\mathrm{XXZ}$ spin chains with a random magnetic field

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 $\Delta ,$ 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 $\Delta .$ 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.