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The antiferromagnetic Ising model on a checkerboard lattice has an ice-likeground state manifold with extensive degeneracy. and, to leading order in J_xy,deconfined spinon excitations. We explore the role of cyclic exchange arisingat 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 forflippable plaquettes - a phase with long range Neel order and confined spinonexcitations, a non-magnetic state of resonating square plaquettes, and aquasi-collinear phase with gapped but deconfined spinon excitations. Therelevance of the results to the square--lattice quantum dimer model is alsodiscussed.Comment: 4 pages, 5 figure

physical review. b, condensed matter and materials physics

Cyclic exchange, isolated states, and spinon deconfinement in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>Heisenberg model on the checkerboard lattice

Cyclic exchange, isolated states, and spinon deconfinement in anXXZHeisenberg model on the checkerboard lattice