Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice

TL;DR

This paper investigates how cyclic exchange interactions influence the phases and spinon excitations in an XXZ Heisenberg model on a checkerboard lattice, revealing three distinct phases with varying magnetic order and spinon confinement.

Contribution

It introduces a mapping to a quantum six-vertex model to analyze phase transitions and spinon behavior in the presence of cyclic exchange on the checkerboard lattice.

Findings

Identification of three distinct phases with different magnetic and spinon properties.

Demonstration of spinon confinement and deconfinement depending on the phase.

Connection of results to the square-lattice quantum dimer model.

Abstract

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order J^2_xy/J_z on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six--vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes - a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating square plaquettes, and a quasi-collinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square--lattice quantum dimer model is also discussed.