Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913822253514752 |
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| author | Pradenas, Bastián Adamyan, Grigor Tchernyshyov, Oleg |
| author_facet | Pradenas, Bastián Adamyan, Grigor Tchernyshyov, Oleg |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice Pradenas, Bastián Adamyan, Grigor Tchernyshyov, Oleg Strongly Correlated Electrons Mesoscale and Nanoscale Physics 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. |
| title | Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2504.12411 |