Quantum Thermal Hall Effect of Chiral Spinons in a Kagome Strip

 I will describe a recent study of a toy model for the thermal Hall effect in a chiral spin liquid. Specifically, we focus on a spin-1/2 system on a strip of Kagome lattice modeled as a three-leg XXZ spin-ladder, where we further introduce a Dzyaloshinskii-Moriya interaction (D) and a tunable magnetic field (B). Using Bosonization to derive a low-energy theory for the spinons in this system, we identify three distinct B-dependent quantum phases: a valence-bond crystal (VBC), a "metallic" spin liquid (MSL) and a chiral spin liquid (CSL). In the presence of a temperature difference between the top and the bottom edges of the strip, we evaluate the net heat current generated along the strip, and consequently the thermal Hall conductivity. We find that the VBC-MSL-CSL transitions are accompanied by a pronounced change in the behavior of thermal Hall coefficient as a function of B. In particular, analogously to the quantum Hall effect, in the CSL phase the thermal Hall conductivity exhibits a quantized plateau centered around a commensurate value of the spinon 'filling factor' B/D.