标题： 三角晶格上的海森堡反铁磁体中的自发对称性破缺 显示英文标题

标题： Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

摘要： 我们对非共线反铁磁体中被忽视的对称结构进行了详细研究，该结构导致了自旋波的涌现量子数。 聚焦于三角晶格海森堡反铁磁体，我们表明其自旋序参数在扩展的对称群 $\mathrm{SO(3)_L \times SO(2)_R}$下变换，而不是传统的自旋旋转群 $\mathrm{SO(3)}$。 尽管这种更大的对称性被基态自发打破，但残余子群仍然存在，导致守恒的诺特电荷，在量化后，使自旋波获得了一个额外的量子数—— \emph{同位旋}——除了能量和动量之外。 我们的结果为理解非共线磁系统中的对称性、简并性和量子数提供了全面的框架，并在非共线反铁磁体中的对称性破缺范式与粒子物理中的手征对称性破缺之间建立了意想不到的联系。 显示英文摘要

摘要： 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.