Analytic study of the U(1) LGT with fermion at finite temperature and density

In this letter, we apply the variational cumulant expansion (VCE) to the U(1) LGT with fermion at finite density (μ ≠ 0), which has a complex action. The order parameters L and L∗ at finite temperature (T ≠ 0) are calculated. Our results are compared with MC results [N. Bilic, H. Gausterer and S. Sanielevici, Phys. Lett. B 198 (1987) 235] suggesting new conclusions which are different from that of the mean field approximation.