Paper detail

Generic quantum spin ice

We consider possible exotic ground states of quantum spin ice as realized in rare earth pyrochlores. Prior work in Phys. Rev. Lett. 108, 037202 introduced a gauge mean field theory (gMFT) to treat spin or pseudospin Hamiltonians for such systems, reformulated as a problem of bosonic spinons coupled to a U(1) gauge field. We extend gMFT to treat the most general, nearest neighbor exchange Hamiltonian, which contains a further exchange interaction, not considered previously. This term leads to interactions between spinons, and requires a significant extension of gMFT, which we provide. As an application, we focus especially on the non-Kramers materials Pr2TM2O7 (TM=Sn, Zr, Hf, and Ir), for which the additional term is especially important, but for which an Ising-planar exchange coupling discussed previously is forbidden by time-reversal symmetry. In this case, when the planar XY exchange is unfrustrated, we perform a full analysis and find three quantum ground states: a U(1) quantum spin liquid (QSL), an antiferro-quadrupolar ordered state and a non-coplanar ferro-quadrupolar ordered one. We also consider the case of frustrated XY exchange, and find that it favors a pi-flux QSL, with an emergent line degeneracy of low energy spinon excitations. This feature greatly enhances the stability of the QSL with respect to classical ordering.