Holes in a quantum antiferromagnet: A formalism and some exact results

This is a detailed version of an earlier communication in which a theory of hole motion in a quantum antiferromagnet was developed and some exact results obtained in d=1. In this picture, hole motion is very naturally restricted to sublattice A or B of a bipartite lattice. Holes in A or B behave like oppositely charged particles coupled to a gauge field driven by the antiferromagnetic fluctuations of the medium. The general picture is studied in detail for d=1, for a finite concentration of holes. The continuum theory is that of a massless Dirac fermion coupled to the nonlinear sigma model field via a gauge coupling. It is found that holes can wipe out the topological θ term, reduce the power law antiferromagnetic correlations to exponentials and show a divergent superconducting susceptibility. The style of the paper is rather pedagogical and intended for a broad readership.