Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature.

Abstract

We examine the phase structure of the two-flavor Schwinger model as a function of the θ angle and the two masses, m_{1} and m_{2}. In particular, we find interesting effects at θ=π: along the SU(2)-invariant line m_{1}=m_{2}=m, in the regime where m is much smaller than the charge g, the theory undergoes logarithmic renormalization group flow of the Berezinskii-Kosterlitz-Thouless type. As a result, dimensional transmutation takes place, leading to a nonperturbatively small mass gap ∼e^{-Ag^{2}/m^{2}}. The SU(2)-invariant line lies within a region of the phase diagram where the charge conjugation symmetry is spontaneously broken and whose boundaries we determine numerically. Our numerical results are obtained using the Hamiltonian lattice gauge formulation that includes the mass shift m_{lat}=m-g^{2}a/4 dictated by the discrete chiral symmetry.