Talk page

Title:
Spontaneous ergodicity breaking in invariant matrix models

Speaker:
Fabio Franchini

Abstract:
We reconsider the status of eigenvectors of a random matrix. Traditionally, the requirement of base invariance has lead to the conclusion that invariant models describe extended 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 U(N) symmetry to a smaller one. Models with log-normal weight, such as the Muttalib ensemble and those emerging in Chern-Simons and ABJM theories, break the U(N) in a critical way, resulting into a multi-fractal eigenvector statistics.

Link:
http://scgp.stonybrook.edu/video_portal/video.php?id=2456

Workshop:
Simons- Program: Statistical mechanics and combinatorics