# Quantized thermal Hall conductance from edge current calculations in lattice models

## TL;DR

This paper introduces a new method to calculate the quantized thermal Hall conductance in lattice models by focusing on edge currents, simplifying the process compared to traditional linear-response approaches.

## Contribution

It proposes an edge current-based approach for computing thermal Hall conductance in chiral topological models, overcoming limitations of the Kubo formula in microscopic simulations.

## Key findings

- Edge current calculation effectively captures quantized thermal Hall conductance.
- The method is validated on chiral p-wave superconductors and Hofstadter models.
- Finite-size effects are analyzed, recommending long strip geometries for simulations.

## Abstract

The quantized thermal Hall effect is an important probe for detecting chiral topological order and revealing the nature of chiral gapless edge states. The standard Kubo formula approach for the thermal Hall conductance $\kappa_{xy}$ based on the linear-response theory faces difficulties in practical application due to the lack of a reliable numerical method for calculating dynamical quantities in microscopic models at finite temperature. In this work, we propose an approach for calculating $\kappa_{xy}$ in two-dimensional lattice models displaying chiral topological order. Our approach targets at the edge current localized at the boundary which involves only thermal averages of local operators in equilibrium, thus drastically lowering the barrier for the calculation of $\kappa_{xy}$. We use the chiral $p$-wave superconductor (with and without disorder) and the Hofstadter model as benchmark examples to illustrate several sources of finite-size effects, and we suggest the infinite (or sufficiently long) strip as the best geometry for carrying out numerical simulations.