Massive Schwinger model at finite $\theta$

Using the approach developed in [V. Azcoiti, G. Di Carlo, A. Galante, V. Laliena, $\mathit{\text{Phys.}}\mathit{\text{Lett.}}$ $\mathbf{\text{B563}}$, (2003) 117], we are able to reconstruct the behavior of the massive 1-flavor Schwinger model with a $\theta$ term and a quantized topological charge. We calculate the full dependence of the order parameter with $\theta$. Our results at $\theta =\pi$ are compatible with Coleman’s conjecture on the phase diagram of this model.