We present an exact formulation of the self-induced effective gauge fields both in the Hubbard model and in the true continuum description of the Cu-O planes of the high-${\mathit{T}}_{\mathit{c}}$ perovskites. We bypass the solution of the ground state in favor of the chirality order parameter as the intrinsic variable. The constraint of gauge symmetry greatly narrows the admissible forms for the gauge fields. We find that these fields can produce broken-symmetry chiral ground states on a lattice, but the intrinsic frustration in the continuum form of the gauge field seems to rule out such a state in the real Cu-O plane.

• Received 16 April 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.1498