Topological Order in Projected Wave Functions and Effective Theories of Quantum Antiferromagnets

TL;DR

This paper investigates topological order in resonating valence bond (RVB) states derived from Gutzwiller projection, revealing conditions under which topological order is absent due to sign rule constraints.

Contribution

It demonstrates that all bipartite effective theory-derived RVB states are positive definite, explaining the universal absence of topological order in these states.

Findings

Projected RVB states from bipartite theories are positive definite.

Absence of topological order explained by Marshall sign rule.

Constructed topological excitations via flux tube insertion.

Abstract

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