Supersymmetric Hubbard Operators

Abstract

We develop a supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single $U(1)\times SU(1|1)$ gauge theory, a group with larger symmetry than the product of two $U(1)$ gauge groups. These representations of the Hubbard operator can be used to incorporate strong Hund's interactions in multi-electron atoms as a constraint. We show how this method can be combined with the $SP(N)$ group to yield a locally supersymmetric large-N formulation of the $t-J$ model.

12 pages, 1 figure. Substantially Revised Version