Localization in a random $x-y$ model with the long-range interaction: Intermediate case between single particle and many-body problems

Understand

Many-body localization in an $XY$ model with a long-range interaction is investigated.

• We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping.
• The combination of hopping and induced Ising interactions for the power law distance dependent hopping $V(R) \propto R^{-\alpha}$ always leads to the localization breakdown in a thermodynamic limit of an infinite system at $\alpha < 3d/2$ where $d$ is a system dimension.
• The delocalization takes place due to the induced Ising interactions $U(R) \propto R^{-2\alpha}$ of &#34;extended&#34; resonant pairs.