Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

Bastián Pradenas; Grigor Adamyan; Oleg Tchernyshyov

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arXiv · 2504.12411

Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

Bastián Pradenas·Grigor Adamyan·Oleg Tchernyshyov

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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, $\mathrm{SO(3)_L \times SO(2)_R}$, rather than the conventional spin-rotation group $\mathrm{SO(3)}$. 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.

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Bastián Pradenas, Grigor Adamyan, Oleg Tchernyshyov. 2025-04-16. Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice. https://arxiv.org/abs/2504.12411

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