Mean-field energies of spin-flux phases.

Abstract

It is suggested that conventional spin-density-wave states for an interacting many-electron system in a two-dimensional square lattice are energetically unstable to the formation of spin flux. Spin flux corresponds to a rotation of the internal coordinate system of the electron as it traverses a closed loop. The flux is dynamically generated by the electromagnetic interaction in the many-body system. This is illustrated by including the nearest-neighbor Coulomb repulsion between electrons in the Hubbard model. Using a Grassmann field theory, we derive the mean-field equations for spin flux and local-moment ordering. For a wide range of Hubbard model couplings U/t and doping \ensuremath{\delta} we find that the generation of spin flux leads to a lowering of the mean-field local-moment amplitude. This suppression of the local moment offsets the additional quantum zero-point energy associated with spin flux and leads to an overall reduction in the total many-electron energy. When the spin-flux vortex filaments are endowed with a quantum dynamics, chiral symmetry breaking is possible. We show that under certain conditions, this leads to a further reduction of local-moment amplitude and many-electron energy.