U(1) and Z₂ spin liquids on the pyrochlore lattice

The geometrically frustrated 3D pyrochlore lattice has been long predicted to host a quantum spin liquid. To this date, most proposals for pyrochlore materials have been a U(1) quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. In this work we explore the possibility of finding spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric U(1) and Z₂ spin liquids on pyrochlore using the projective symmetry group method for the fermionic spinons. We find 22 and 28 classes for the U(1) and the Z₂ types without considering time reversal, while upon adding time reversal the numbers of classes become 16 and 48, respectively. For each class the most general symmetry-allowed spinon mean-field Hamiltonian is given. We find that several U(1) classes possess an unusual gapless multi-nodal line structure in the spinon bands, which is protected by the (projective) three-fold rotation and screw symmetries of the pyrochlore space group. Via a toy model, we consider the effect of gauge fluctuations for such a nodal structure and study the various thermodynamic properties of this system.