Non-ergodic behaviour of Anderson insulators with and without Coulomb interactions

Abstract

In some recent papers in which Monte Carlo methods have been used, it has been found that disordered Anderson insulators with Coulomb interactions may become glassy at low temperatures. This was indicated by a non-vanishing value of an order parameter. In the present paper, the transition to a glassy state is investigated analytically for systems with and without Coulomb interactions. For the purposes of the analysis, a system is taken to be in the glassy state if it fails to satisfy the ergodic hypothesis. A transition to non-ergodic behaviour is found for both interacting and non-interacting systems, but the transition for the interacting system is softer and occurs at a higher temperature. The results are subject to certain approximations and assumptions, which are specified.