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 $ϵ$ restores spinon confinement at $T=0$. We demonstrate that deconfinement is recovered in the finite-temperature region $ϵ⪡T⪡J$, 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 by taking into account their nonorthogonality. We find that in these systems, nearest-neighbor exchange interactions do not lead to Rokhsar-Kivelson-type processes.