Abstract

Spin liquids are magnetic states of matter with do not order even at the lowest temperatures, but instead feature strong, correlated fluctuations which are effectively described by an emergent gauge theory. Members of the family of materials called rare-earth Pyrochlores (R$_2$M$_2$O$_7$) have been known to host a classical spin liquid phase for a long time. Most prominently, the so-called “spin ice” compounds Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ realize an emergent Maxwell theory at low temperatures, with excitations taking the form of magnetic monopoles. Recent experiments on the cerium-based Pyrochlores Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$ suggest that these materials may realize a quantum version of the this phase called “quantum spin ice”. In this talk, I focus on the theoretical description of cerium-based Pyrochlores. Their most general symmetry-allowed exchange Hamiltonian takes a remarkably simple form, that is a XYZ model on the Pyrochlore lattice. This allows us to make reliable numerical predictions for all available experimental measurements in the full phase diagram of this model and, in turn, to obtain reliable estimates for the Hamiltonian parameters for real materials. Along the way, we also gain new insights into the ground state phase diagram of the theory model.