# Intrinsic Thermal Hall Effect in Mott Insulators

**Authors:** Jixun K. Ding, Emily Z. Zhang, Wen O. Wang, Tessa Cookmeyer, Brian Moritz, Yong Baek Kim, Thomas P. Devereaux  
**arXiv:** [2410.14863](https://arxiv.org/abs/2410.14863)  
**Date:** 2024-10-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2410.14863v1/

## Key points

- Study by Jixun K. Ding et al. explores intrinsic thermal Hall effect in Mott insulators
- Research prompted by recent experimental findings of significant thermal Hall effect in square lattice antiferromagnetic Mott insulators
- Objective was to determine if simple Mott insulator could sustain a finite thermal Hall effect
- Initial calculations with spin-only model suggested negative answer, but quantum Monte Carlo simulations showed support for finite thermal Hall effect under specific conditions
- Observing a finite thermal Hall effect requires time-reversal and particle-hole symmetry breaking
- Physical mechanism for finite transverse thermal conductivity illustrated through magnon-magnon scattering analysis using semi-classical Boltzmann approach
- Findings challenge conventional beliefs about square and triangular lattices with SU(2) symmetry not exhibiting a finite thermal Hall effect
- Research emphasizes importance of considering magnon contributions in analyzing thermal properties of insulating magnets

## Summary

The study conducted by Jixun K. Ding, Emily Z. Zhang, Wen O. Wang, Tessa Cookmeyer, Brian Moritz, Yong Baek Kim, and Thomas P. Devereaux delves into the intrinsic thermal Hall effect in Mott insulators. The research was prompted by recent experimental findings that suggested a significant thermal Hall effect in square lattice antiferromagnetic Mott insulators. The primary objective was to determine if a simple Mott insulator could indeed sustain a finite thermal Hall effect. Initially, calculations within a spin-only low-energy effective spin model with non-interacting magnons indicated that the answer was negative. However, through the utilization of determinant quantum Monte Carlo simulations, the researchers were able to demonstrate that the single-band $t$-$t'$-$U$ Hubbard model coupled to an orbital magnetic field could support a finite thermal Hall effect under specific conditions where $t' \neq 0$ and $B \neq 0$ in the Mott insulating phase. The study also highlighted that observing a finite thermal Hall effect necessitates time-reversal and particle-hole symmetry breaking. By analyzing magnon-magnon scattering using a semi-classical Boltzmann approach, the researchers illustrated a physical mechanism through which finite transverse thermal conductivity could arise. These findings challenge conventional beliefs that square and triangular lattices with SU(2) symmetry do not exhibit a finite thermal Hall effect. In conclusion, this research calls for a critical re-examination of thermal Hall effect data in insulating magnets as it emphasizes the importance of considering magnon contributions rather than excluding them outright. The comprehensive analysis presented in this study provides valuable insights into the complex behavior of thermal properties in Mott insulators and opens up new avenues for further exploration in this field of study.