Phase Transitions of Fermions Coupled to a Gauge Field: a Quantum Monte Carlo Approach

Abstract

A grand canonical system of non-interacting fermions on a square lattice is considered at zero temperature. Three different phases exist: an empty lattice, a completely filled lattice and a liquid phase which interpolates between the other two phases. The Fermi statistics can be changed into a Bose statistics by coupling a statistical gauge field to the fermions. Using a quantum Monte Carlo method we investigate the effect of the gauge field on the critical properties of the lattice fermions. It turns out that there is no significant change of the phase diagram or the density of particles due to the gauge field even at the critical points. This result supports a recent conjecture by Huang and Wu that certain properties of a three-dimensional flux line system (which is equivalent to two-dimensional hard-core bosons) can be explained with non-interacting fermion models.