Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling

TL;DR

This paper investigates many-body localization in disordered spin systems with long-range interactions, combining analytical theory and finite size numerical scaling to understand the conditions for localization and delocalization.

Contribution

It provides a combined analytical and numerical analysis of many-body localization with long-range interactions, revealing universal scaling laws for the critical disorder strength.

Findings

Localization absent for $ ext{alpha}<2d$ in infinite systems

Critical disorder scales as $W_c \, \propto \, N^{(2d-\alpha)/d}$

Finite size effects induce delocalization in small systems

Abstract

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact numerical solutions with a number of spins $N$. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for $d$-dimensional system including the absence of localization in the infinite system at $\alpha<2d$ and a universal scaling of a critical energy disordering $W_{c} \propto N^{\frac{2d-\alpha}{d}}$. %The finite size effect on the interaction stimulated delocalization of energy in the ensemble of interacting two level systems in amorphous solids at low temperature is discussed.