Exact solution of a quantum gauge magnet in 2+1 dimensions

A parity-violating U(1) gauge magnet hamiltonian on a two-dimensional lattice is mapped to a problem of transversely oscillating, non-overlapping strings. The one-string problem is found to be equivalent to a modified XX spin chain. The multi-string eigenstates and eigenvalues are found explicitly. A critical point at which the excitations become gapless is shown to exist. The ground-state energy is calculated on a finite cylinder of arbitrary dimensions. Charge is found to be confined for all couplings. It is argued that this model is a lattice version of electrodynamics with a Chern-Simons term in a strongly coupled phase. (orig.)