Thermal Hall response of an abelian chiral spin liquid at finite temperatures

TL;DR

This paper investigates the thermal Hall effect in an abelian chiral spin liquid derived from a kagome lattice Heisenberg antiferromagnet, revealing quantized responses at low temperatures and power-law behavior with logarithmic corrections at higher temperatures.

Contribution

It provides explicit finite-temperature expressions for thermal Hall conductivity in a gapped abelian chiral spin liquid using a large-N approach, including matter and gauge fluctuations.

Findings

Quantized thermal Hall response at low temperatures matches conformal field theory predictions.

Power-law behavior with logarithmic corrections in the quantum critical regime.

Provides a framework for understanding thermal Hall response at higher temperatures.

Abstract

Thermal Hall transport has emerged as a valuable tool for probing the fractionalized excitations in chiral quantum spin liquids. Observing quantized thermal Hall response, expected at temperatures below the spectral gap, has been challenging and controversial. The finite temperature behavior, especially in the quantum critical regime above the spectral gap, can provide useful signatures of the underlying topological order. In this context, we study the spin-$1/2$ Heisenberg antiferromagnet on a kagome lattice that is believed to be a U$(1)$ Dirac spin liquid over a wide intermediate energy range. Scalar spin chirality perturbations turn this into a gapped abelian chiral spin liquid (CSL) with semionic topological order. Using a recently developed large-$N$ technique [Guo et al., Phys. Rev. B 101, 195126 (2020)], we obtain explicit expressions for the thermal Hall conductivity $\kappa_{xy}$ at finite temperatures taking into account both matter and gauge fluctuations. At low temperatures below the spectral gap, the quantized thermal Hall response agrees with that expected from conformal field theory and gravitational anomaly arguments. Our main finding is that in a large temperature window spanning the spectral gap and the Curie temperature scales where quantum critical fluctuations dominate, $\kappa_{xy}/T$ obeys a power-law with logarithmic corrections. Our analysis also provides a route to understanding the thermal Hall response at higher temperatures in the quantum critical regime.