Self-consistent approach to many-body localization and subdiffusion

Understand

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization.

• Results show a qualitative agreement with numerically obtained dynamical structure factor in the whole range of frequencies and wavevectors, as well as across the transition to the nonergodic behavior.
• The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity $\sigma(\omega) \propto |\omega|^\alpha$, i.e., with vanishing d.c.
• limit $\sigma_0=0$ and $\alpha<1$ varying with disorder, while we get $\alpha >1$ in the localized phase.