# Enhanced thermal Hall effect in the square-lattice Néel state

## Abstract

Common wisdom about conventional antiferromagnets is that their low-energy physics is governed by spin–wave excitations. However, recent experiments on several cuprate compounds have challenged this concept. An enhanced thermal Hall response in the pseudogap phase was identified, which persists even in the insulating parent compounds without doping. Here, to explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining Néel state to a state with coexisting Néel 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 Néel state to the critical point can explain the enhanced thermal Hall effect seen in experiments.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

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## Acknowledgements

This research was supported by the National Science Foundation under grant no. DMR-1664842. S.C. acknowledges support from the ERC synergy grant UQUAM. M.S.S. acknowledges support from the German National Academy of Sciences Leopoldina through grant no. LPDS 2016-12. We thank N. Seiberg for explaining many subtle aspects of the non-Abelian dualities to us. We thank G. Grissonnanche, Y.-C. He, C. Hickey, C.-M. Jian, P. A. Lee, A. Nahum, L. Taillefer and L. Zou for helpful discussions.

## Author information

All authors contributed to the research leading to the formulation and analyses of the quantum field theory and the writing of the paper. R.S. performed the numerical mean-field computations presented in Figs. 2 and 3.

Correspondence to Subir Sachdev.

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## Supplementary information

### Supplementary Materials

Supplementary Fig. 1, text and references.

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