Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice

TL;DR

This paper demonstrates a quantum phase transition in a kagome lattice model of hard-core bosons, revealing a $Z_2$ topologically ordered spin-liquid phase with fractionalized excitations, supported by quantum Monte Carlo simulations.

Contribution

It provides the first numerical evidence of a $Z_2$ spin-liquid phase in an easy-axis $S=1/2$ model without special conservation laws on the kagome lattice.

Findings

Identified a continuous superfluid-insulator transition with specific critical exponents.

Found the insulator exhibits topological order and short-range correlations.

Estimated the vison gap indicating fractionalized excitations.

Abstract

We study a model of hard-core bosons with short-range repulsive interactions at half-filling on the kagome lattice. Using quantum Monte Carlo (QMC) numerics, we find that this model shows a continuous superfluid to insulator quantum phase transition, with exponents $z=1$ and $\nu\approx 0.67(5)$. The insulator, $\cI^*$, exhibits short-ranged density and bond correlations, topological order and exponentially decaying spatial vison correlations, all of which point to a $Z_2$ fractionalized phase. We estimate the vison gap in $\cI^*$ from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and $S=1/2$ spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/2 model with no special conservation laws.