# Enhanced thermal Hall effect in the square-lattice N\'eel state

## TL;DR

This paper investigates the quantum phase transition in a square-lattice antiferromagnet to explain the experimentally observed enhanced thermal Hall effect in cuprate compounds, linking topological order and criticality.

## Contribution

It introduces a novel theoretical framework describing a transition from a Nél state to a state with semion topological order, explaining experimental thermal Hall observations.

## Key findings

- Critical point described by a strongly-coupled conformal field theory
- Four dual formulations relate gauge theories to lattice degrees of freedom
- Proximity to the critical point accounts for enhanced thermal Hall effect

## Abstract

Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining N\'eel state to a state with coexisting N\'eel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global $SO(3)$ symmetry. The field theory has four different formulations in terms of $SU(2)$ or $U(1)$ gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining N\'eel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.