Vortex patterns and infinite degeneracy in the uniformly frustrated XY models and lattice Coulomb gas

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 m>or=3 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.