Single-particle excitations across the many-body localization transition in quasi-periodic systems

Abstract

We study many-body localization transition in one dimensional systems in the presence of a deterministic quasi-periodic potential. We focus on single-particle excitations produced in highly excited many-body eigenstates obtained through single-particle Green's function in real space. A finite-size scaling analysis of the ratio of the typical to average value of the local density of states of single particle excitations is performed assuming that the correlation length $\xi$ diverges at the transition point with a power-law $\xi \sim |h-h_c|^{-\nu}$. Both for the Aubry-Andre (AA) model and the generalized AA model, the finite size scaling of the local density of states obeys the single parameter scaling. A good quality scaling collapse is obtained for $\nu \ge 1$ which satisfies the generalized Luck's criterion for quasiperiodic systems. This analysis supports the continuous nature of the many-body localization transition in systems with AA and generalized AA potentials.Comment: 10 pages, 11 figure