Solvable Quantum Grassmann matrices

Abstract

We explore systems with a large number of fermionic degrees of freedomsubject to non-local interactions. We study both vector and matrix-like modelswith quartic interactions. The exact thermal partition function is expressed interms of an ordinary bosonic integral, which has an eigenvalue repulsion term inthe matrix case. We calculate real time correlations at finite temperature andanalyze the thermal phase structure. When possible, calculations are performedin both the original Hilbert space as well as the bosonic picture, and the exactmap between the two is explained. At large N, there is a phase transition toa highly entropic high temperature phase from a low temperature low entropyphase. Thermal two-point functions decay in time in the high temperature phase.