Quantum Phases in an SU(2) YM Matrix Model Coupled with Fermions

By investigating the $SU(2)$ Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. These we interpret as different quantum phases in the theory.