Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

We present a detailed investigation of an overlooked symmetry structure in noncollinear 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 SO(3)L×SO(2)R, rather than the conventional spin-rotation group 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, isospin, beyond their energy and momentum. Our results provide a comprehensive framework for understanding symmetry, degeneracy, and quantum numbers in noncollinear magnetic systems, and bridge an unexpected connection between the paradigms of symmetry breaking in noncollinear antiferromagnets and chiral symmetry breaking in particle physics.