Semiclassical theory for quantum spin models with ring exchange on the triangular lattice

TL;DR

This paper develops a semiclassical framework for quantum spin models with ring exchange on the triangular lattice, revealing topological phenomena and differences in ground states based on spin parity.

Contribution

It introduces a semiclassical theory capturing $Z_2$ vortices and their geometric phases, linking topological degeneracy to spin parity and connecting to dimer models.

Findings

Identification of $Z_2$ vortices and their geometric phases.

Topological degeneracy depends on whether 2S is odd or even.

Connection established between spin models and dimer models.

Abstract

A semiclassical theory of a quantum spin$-S$ model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of $Z_2$ vortices is exhibited. The vortices are shown to carry a nontrivial geometric phase for the order parameter when $2S$ is odd, leading to a difference between the quantum disordered ground states and low energy spectra for half odd integer and half even integer spin systems, and a topological degeneracy on surfaces with nontrivial cycles. A connection to dimer models is discussed.