Topological order in Gutzwiller-projected wave functions for quantum antiferromagnets

Abstract

We study the topological order in a resonating valence bond (RVB) state derived from the Gutzwiller projection of the BCS-like mean-field state. We propose the construction of the topological excitation on the projected RVB state through the Gutzwiller projection of the mean-field state with inserted ${Z}_{2}$ flux tube. We prove that all projected RVB states derived from bipartite effective theories, no matter what the gauge structure in the mean-field ansatz is, are positive definite in the sense of the Marshall sign rule, which provides a universal origin for the absence of topological order in such an RVB state.