Events at Physics |
Due to a broad phase transition between the FCI and the superconducting state, we further study the effect of phase fluctuations on the $Z_3$ parafermions, using field-theoretical methods as well as the density-matrix renormalization group. We find a rich phase diagram composed of Mott insulating phases and two distinct Luttinger liquids, whose fundamental excitations carry charges 2e and 2e/3, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $Z_3\times\text{U(1)}$ second-order phase transition characterized by central charge c = 9/5.