engleski

Spontaneous Ergodicity Breaking in Invariant Matrix Models

Many physical systems are ergodic, meaning that, over time, they sample most allowed physical states. Ergodicity is a central tenant for thermodynamics, as it provide meaning to the concept of equilibrium. However, certain systems are not ergodic and thus posses peculiar and important properties. Non-ergodic systems are typically harder to study. Here, we propose a new approach to the study of ergodicity breaking and localization, based on an abstract formulation that can disclose powerful computational techniques. Such formulation is grounded in the field of random matrix theory, but moves beyond the standard assumption that invariant models describe only extended (ergodic) systems. We show that deviations of the eigenvalue statistics from the Wigner-Dyson universality reflects itself on the eigenvector distribution. In particular, gaps in the eigenvalue density spontaneously break the rotational symmetry of the model to a smaller one, hence rendering the system not ergodic anymore. Models with log-normal weights, recently considered also in string theory models such as ABJM theories, show a critical eigenvalue distribution which indicates a critical breaking of the symmetry. While the main motivation for this approach is the description of the critical phase of a disordered conductive systems (Anderson Metal/Insulator transition), the underlying picture is very general: the spontaneous breaking of rotational symmetry corresponds to clustering of different physical degrees of freedom, which, not being equivalent anymore, prevent the exploration of the whole configurational space.

Random Matrices ; Ergodicity Breaking ; Spontaneous Symmetry Breaking

nije evidentirano