Character Expansion, Zeros of Partition Function and $θ$-term in U(1) Gauge Theory

Abstract

Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with $þ$-term in 2 dimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussian form at any $\b$(inverse coupling constant). The partition function $Z(þ)$ at large volume is shown to be given by the elliptic theta function. It provides the information of the zeros of partition function as an analytic function of $\ze= e^{i þ}$ ($þ$ = theta parameter). These partition function zeros lead to the phase transition at $þ=π$. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i)``set method" and (ii)``trial function method".