# Kagome model for a ${\mathbb Z}_2$ quantum spin liquid

## TL;DR

This paper introduces a sign-problem-free model on the Kagome lattice that exhibits a gapped ${\mathbb Z}_2$ topological quantum spin liquid, supported by numerical evidence including entanglement entropy analysis.

## Contribution

The study presents a novel, sign-problem-free Kagome lattice model that demonstrates a gapped ${\mathbb Z}_2$ quantum spin liquid phase, with insights from large-$N$ analysis and entanglement entropy.

## Key findings

- Identification of a quantum spin liquid phase in the model
- Evidence of a gapped ${\mathbb Z}_2$ topological phase
- Numerical confirmation via entanglement entropy

## Abstract

We present a study of a simple model antiferromagnet consisting of a sum of nearest neighbor SO($N$) singlet projectors on the Kagome lattice. Our model shares some features with the popular $S=1/2$ Kagome antiferromagnet but is specifically designed to be free of the sign-problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb Z}_2$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.