High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets

The ground states of Klein type spin models on the pyrochlore and checkerboard lattice are spanned by the set of singlet dimer coverings, and thus possess an extensive ground--state degeneracy. Among the many exotic consequences is the presence of deconfined fractional excitations (spinons) which propagate through the entire system. While a realistic electronic model on the pyrochlore lattice is close to the Klein point, this point is in fact inherently unstable because any perturbation $\epsilon$ restores spinon confinement at $T = 0$. We demonstrate that deconfinement is recovered in the finite--temperature region $\epsilon \ll T \ll J$, where the deconfined phase can be characterized as a dilute Coulomb gas of thermally excited spinons. We investigate the zero--temperature phase diagram away from the Klein point by means of a variational approach based on the singlet dimer coverings of the pyrochlore lattices and taking into account their non--orthogonality. We find that in these systems, nearest neighbor exchange interactions do not lead to Rokhsar-Kivelson type processes.