Hidden non-Abelian gauge symmetries in doped planar antiferromagnets

Abstract

We investigate the possibility of hidden non-Abelian local phase symmetries in large-$U$ doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge separation ansatz, appropriate to incorporate holon spin flip, which allows for such a hidden local gauge symmetry to emerge in the effective action. The group is of the form ${\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}}_{S}(1)\ensuremath{\bigotimes}{\mathrm{U}}_{\mathrm{em}}(1),$ where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, ${\mathrm{U}}_{\mathrm{em}}(1)$ is that of ordinary electromagnetism, associated with the electric charge of the holes, and ${\mathrm{U}}_{S}(1)$ is a ``statistical'' Abelian gauge group pertaining to the fractional statistics of holes on the spatial plane. In certain regime of the parameters of the model, namely, strong ${\mathrm{U}}_{S}(1)$ and weak SU(2), there is the possibility of dynamical formation of a holon condensate. This leads to a dynamical breaking of $\mathrm{SU}(2)\ensuremath{\rightarrow}\mathrm{U}(1).$ The resulting Abelian effective theory is closely related to an earlier model proposed as the continuum limit of large-spin planar doped antiferromagnets, which lead to an unconventional scenario for two-dimensional parity-invariant superconductivity.