# Quantum Thermal Hall effect of chiral spinons on a Kagome strip

## TL;DR

This paper develops a theoretical model for the thermal Hall effect in a Kagome strip with chiral spin interactions, identifying phase-dependent behaviors and a quantized plateau in thermal conductivity related to spinon filling.

## Contribution

It introduces a low-energy bosonization-based theory for spinons in a Kagome strip, revealing phase transitions and quantized thermal Hall conductance in a chiral spin liquid.

## Key findings

- Identification of three quantum phases: VBC, MSL, CSL.
- Observation of a quantized plateau in thermal Hall conductivity in the CSL phase.
- Qualitative change in $_{xy}$ behavior across phase transitions.

## Abstract

We develop a theory for the thermal Hall coefficient in a spin-$\frac{1}{2}$ system on a strip of Kagome lattice, where a chiral spin-interaction term is present. To this end, we model the Kagome strip as a three-leg $XXZ$ spin-ladder, and use Bosonization to derive a low-energy theory for the spinons in this system. Introducing further a Dzyaloshinskii-Moriya interaction ($D$) and a tunable magnetic field ($B$), 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 $\Delta T$ between the top and the bottom edges of the strip, we evaluate the net heat current $J_h$ along the strip, and consequently the thermal Hall conductivity $\kappa_{xy}$. We find that the VBC-MSL-CSL transitions are accompanied by a pronounced qualitative change in the behavior of $\kappa_{xy}$ as a function of $B$. In particular, analogously to the quantum Hall effect, $\kappa_{xy}$ in the CSL phase exhibits a quantized plateau centered around a commensurate value of the spinon filling factor $\nu_s\propto B/D$.