Spreading Spin at No Charge: the Thermal Hall Effect in a Quantum Spin Liquid

In solid materials where electrons are strongly interacting, their spin and charge may effectively split to separate degrees of freedom. An extreme manifestation of this phenomena is the complete freezing of the charge degree of freedom (which renders the material electric insulator) while charge-neutral spin excitations are potentially free to move. When such materials possess a crystalline structure that frustrates magnetic ordering, novel phases of matter can form at low temperatures due to the quantum nature of the spin degrees of freedom. Among the most exotic states of matter emerging in these systems are the so-called "spin liquid" phases. Under appropriate conditions, they possess an intriguing signature: a thermal Hall effect in the absence of electric current. I will describe a particular model for spin-1/2 particles on a frustrated lattice which supports such quantum phases, and the behavior of the resulting thermal Hall conductance in the presence of an external magnetic field. Most prominently, we find that tuning the magnetic field induces transitions among three distinct phases: a spin-insulating valence bond crystal, a metallic spin-liquid and a chiral spin-liquid; the latter is an analogue of a quantum Hall liquid in two-dimensional conductors. I will finally discuss the possible relation of these findings to experimental observations of the recent years.