Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice
Abstract
We present a detailed investigation of an overlooked symmetry structure in non-collinear antiferromagnets that gives rise to an emergent quantum number for magnons. Focusing on the triangular-lattice Heisenberg antiferromagnet, we show that its spin order parameter transforms under an enlarged symmetry group, , rather than the conventional spin-rotation group . Although this larger symmetry is spontaneously broken by the ground state, a residual subgroup survives, leading to conserved Noether charges that, upon quantization, endow magnons with an additional quantum number -- \emph{isospin} -- beyond their energy and momentum. Our results provide a comprehensive framework for understanding symmetry, degeneracy, and quantum numbers in non-collinear magnetic systems, and bridge an unexpected connection between the paradigms of symmetry breaking in non-collinear antiferromagnets and chiral symmetry breaking in particle physics.
Keywords
Cite
@article{arxiv.2504.12411,
title = {Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice},
author = {Bastián Pradenas and Grigor Adamyan and Oleg Tchernyshyov},
journal= {arXiv preprint arXiv:2504.12411},
year = {2025}
}