Dynamical spin conductivity in disordered quantum spin chains

Localization caused by disorder has a long history of study since the pioneering work of Anderson. Recently many-body localization (MBL) has been intensively studied in the field of both condensed-matter and statistical physics. Considering the detection of MBL in experiments, it is an important task to investigate on the behavior of physical quantities, especially dynamical ones, in interacting disordered systems. We study the dynamical spin conductivity in XXZ antiferromagnets with random magnetic field. We start from the XX models, which is equivalent to the free fermion system, and then include an Ising interaction. The ground state of easy-plane XXZ chains is gapless Luttinger liquid, and the system is localized by disorder when the Luttinger parameter satisfies K<3/2. We calculate dynamical spin conductivity numerically using the technique of Chebyshev matrix product states. We investigate this quantity in the low and high frequency region, and the behavior is power law in both regions. The power depends on the strength of Ising interaction in the high frequency region.