Topological Order in Gutzwiller Projected Wave Functions for Quantum Antiferromagnets

TL;DR

This paper investigates topological order in resonating valence bond (RVB) states derived from Gutzwiller projection of BCS-like mean field states, revealing conditions under which topological order is absent.

Contribution

It introduces a method to construct topological excitations via Gutzwiller projection with flux insertion and proves a universal sign rule explaining the absence of topological order in bipartite RVB states.

Findings

All bipartite RVB states satisfy the Marshall sign rule.

Bipartite effective theories do not exhibit topological order.

Universal origin of absence of topological order in these states.

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.