近日，山西大学潘建松团队研究了类碱土金属原子中受射影时空反演对称保护的拓扑相。2025年6月3日出版的《物理评论A》杂志发表了这项成果。

拓扑相分类的一个重要方面是系统是无自旋的还是有自旋的，因为这些类表现出不同的对称代数，导致不同的拓扑分类。通过利用投影表示策略，可以使用增强规范场的自旋（或无自旋）系统来模拟无自旋（或有自旋）系统的拓扑相位。在这项研究中，课题组建议使用合成的无自旋碱土金属类原子来实现由自旋模型固有的独特投影时空反演对称性所保障的拓扑相位。 

利用轨道和核自旋自由度的分离，该模型被配置为一个矩形管，均匀的磁通量穿过每个平台，模拟了一个具有投影时空反演对称性的无自旋梯子，满足有自旋模型的代数性质。对于具有轨道间自旋交换相互作用的相互作用拓扑相，它也遵循时空反转对称性，边缘模的四倍简并被分为两对具有两倍简并的边缘模。最后，研究组绘制了完整的相图，发现这些相互作用的拓扑相最终通过自发对称破缺演变为不同的电荷密度波相。

附：英文原文

Title: Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms

Author: Xiaofan Zhou, Suotang Jia, Jian-Song Pan

Issue&Volume: 2025/06/03

Abstract: An important aspect in categorizing topological phases is whether the system is spinless or spinful, given that these classes exhibit distinct symmetry algebras, leading to disparate topological classifications. By utilizing the projective presentation strategy, the topological phases of spinless (or spinful) systems can be emulated using spinful (or spinless) systems augmented with gauge fields. In this study, we propose to implement the topological phases safeguarded by the unique projective space-time inversion symmetry inherent to spinful models, using synthetic spinless alkaline-earth-metal-like atoms. Employing the separation of orbital and nuclear-spin degrees of freedom, the model is configured as a rectangular tube penetrated by a uniform magnetic flux through each plaquette, which simulates a spinless ladder endowed with projective space-time inversion symmetry satisfying the algebraic properties of a spinful model. For interacting topological phases with interorbital spin-exchange interactions, which also adhere to space-time inversion symmetry, the four-fold degeneracy of edge modes is split into two pairs of edge modes with two-fold degeneracy. We map the complete phase diagram in the end and discover that these interacting topological phases ultimately evolve into distinct charge-density-wave phases via spontaneous symmetry breaking.

DOI: 10.1103/PhysRevA.111.063301

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.063301