Testing for topological order in variational wavefunctions for Z(2) spin liquids

TL;DR

This paper establishes criteria to identify Z(2) fractionalization in Gutzwiller projected BCS states representing spin-liquid Mott insulators, using overlap calculations of vortex states, with implications for numerical and experimental studies.

Contribution

It introduces a method to determine Z(2) fractionalization in variational wavefunctions by analyzing vortex state overlaps, advancing understanding of spin-liquid phases.

Findings

Overlap vanishes in the thermodynamic limit indicating Z(2) fractionalization.

Constructed a trial vison state via vortex threading.

Results relevant to numerical models and flux-trapping experiments.

Abstract

We determine the conditions under which a spin-liquid Mott insulator |0> defined by a Gutzwiller projected BCS state at half-filling is Z(2) fractionalized. We construct a trial vison [Z(2) vortex] state |V> by projecting an (hc/2e) vortex threading the hole of a cylinder/torus and examine its overlap with |0> using analytical and numerical calculations. We find that generically the overlap vanishes in the thermodynamic limit, so the spin-liquid is Z(2) fractionalized. We point out the relevance of these results to numerical studies of Hubbard-like models and spin models which have been recently reported to possess spin liquid phases. We also consider possible implications for flux-trapping experiments that have tested for Z(2) fractionalization in underdoped high temperature superconductors.