Monte Carlo study of Schwinger model without the sign problem

Monte Carlo study of the Schwinger model (quantum electrodynamics in one spatial dimension) with a topological $\theta$ term is very difficult due to the sign problem in the conventional lattice formulation. In this paper, we point out that this problem can be circumvented by utilizing the lattice formulation of the bosonized Schwinger model, initially invented by Bender et al. in 1985. After conducting a detailed review of their lattice formulation, we explicitly validate its correctness through detailed comparisons with analytical and previous numerical results at $\theta = 0$. We also obtain the $\theta$ dependence of the chiral condensate and successfully reproduce the mass perturbation result for small fermion masses $m / g \lesssim 0.125$. As an application, we perform a precise calculation of the string tension and quantitatively reveal the confining properties in the Schwigner model at finite temperature and $\theta$ region for the first time. In particular, we find that the string tension is negative for noninteger probe charges around $\theta = \pi$ at low temperatures.