Vortex patterns and infinite degeneracy in the uniformly frustrated XY models and lattice Coulomb gas -: art. no. 046120

We find analytically and numerically that there exist infinite degeneracies in the ground state vortex configurations of a uniformly frustrated XY model on a square lattice for cases of frustrations f = 1/6, 1/7, 1/8, and 1/10. More generally, we could also obtain a class of exact solutions for the phase configurations corresponding to the cases of f = 1/q = 1/(2m) with an integer mgreater than or equal to3 of which the above cases of m = 3, 4, and 5 correspond to the true ground states. These states are analogous to the staircase solutions originally given by Halsey [Phys. Rev. B 31, 5728 (1985)], which, however, are relevant in a different regime of the frustration parameter (or vortex density). In these quasistaircase states, all the gauge-invariant phase differences are found to be integer multiples of pi/2q. The supercurrents are conserved at each node in a trivial manner by separate channels. The infinite ground state degeneracy is preserved in the case of an arbitrary screening length for the corresponding lattice Coulomb gas.