Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states

TL;DR

This paper investigates the topological entanglement entropy of various spin liquid and Laughlin states, confirming their topological order and quantum dimensions through Monte Carlo simulations.

Contribution

It demonstrates the use of topological entanglement entropy to identify topological order in lattice wave-functions of spin liquids and Laughlin states, with results matching theoretical predictions.

Findings

Topological entanglement entropy confirms topological order in chiral and Z2 spin liquids.

Results agree with field theoretic predictions within 4% accuracy.

Monte Carlo calculations on a 12x12 lattice effectively extract topological invariants.

Abstract

We study entanglement properties of candidate wave-functions for SU(2) symmetric gapped spin liquids and Laughlin states. These wave-functions are obtained by the Gutzwiller projection technique. Using Topological Entanglement Entropy \gamma\ as a tool, we establish topological order in chiral spin liquid and Z2 spin liquid wave-functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result \gamma =log D where D is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a 12 times 12 lattice enabling us to extract \gamma\ with small finite size effects. For a chiral spin liquid wave-function, the calculated value is within 4% of the ideal value. We also find good agreement for a lattice version of the Laughlin \nu =1/3 phase with the expected \gamma=log \sqrt{3}.