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 $SU(2)\otimes U_S(1)\otimes U_E(1)$, where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, U_E(1) is that of ordinary electromagnetism, associated with the electric charge of the holes, and U_S(1) is a `statistical' Abelian gauge group pertaining to the fractional statistics of holes on the spatial plane. In a certain regime of the parameters of the model, namely strong 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 $SU(2)\to U(1)$. 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.

Comments: 32 pages LATEX, one figure. (More details given in the passage from the Hubbard model to the long wavelength lattice gauge theory; one figure added; no changes in the conclusions.)