Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice

TL;DR

This study uses variational Monte Carlo methods to identify a gapped chiral spin liquid state with topological order in an extended Heisenberg model on the Kagome lattice, revealing a novel quantum phase.

Contribution

It demonstrates that including second- and third-neighbor interactions stabilizes a chiral spin liquid with non-trivial topological properties, advancing understanding of quantum spin liquids.

Findings

Gapped chiral spin liquid is energetically favored over gapless states.

The flux state exhibits a fractionalized Chern number of 1/2.

Ground state degeneracy confirms topological order.

Abstract

We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with $C=1/2$ fractionalized Chern number.