Nonperturbative Functional Renormalization-Group Approach to the Sine-Gordon Model and the Lukyanov-Zamolodchikov Conjecture

We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value < e((i/2)n beta phi)> of the exponential fields in the massive phase (n is integer and 2 pi/beta denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.