广义$N$态时钟模型中无基态简并的自发对称性破缺
Spontaneous symmetry breaking without ground state degeneracy in generalized $N$-state clock model
AI总结：
本研究探讨了$N$态时钟模型的扩展，发现在周期性边界条件下，即使相展现两极限不可交换性，基态也可唯一且激发态有能隙，从而对自发对称性破缺的标准理解提出质疑。
摘要：
自发对称性破缺是自然界中普遍存在的现象。对称性破缺相的一个决定性特征是，大系统尺寸极限与外场趋于零的极限不可交换。在本研究中，我们探讨了$N$态时钟模型的一族扩展。我们发现，尽管模型具有明显的平移对称性，但在周期性边界条件下，其精确对称性与基态简并度严重依赖于系统尺寸。具体而言，即使相展现出这两种极限的不可交换性，基态也可以是唯一的，且所有激发态都是有能隙的。因此，我们的模型对自发对称性破缺的标准理解提出了质疑。
英文摘要：
Spontaneous symmetry breaking is ubiquitous phenomenon in nature. One of the defining features of symmetry broken phases is that the large system size limit and the vanishing external field limit do not commute. In this work, we study a family of extensions of the $N$-state clock model. We find that the exact symmetry and the ground state degeneracy under the periodic boundary condition heavily depend on the system size, although the model has the manifest translation symmetry. In particular, the ground state can be unique and all excitations are gapped even when the phase exhibits non-commutativity of the two limits. Our model hence poses a question on the standard understanding of spontaneous symmetry breaking.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
