Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a θ term

We make an analysis of the two-dimensional U(1) lattice gauge theory with a theta term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at theta = pi toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L x L = 1024 x 1024 allows us to determine the phase transition at theta = pi is the first order.