标题： 一维多体费米系统中晶体等价的拓扑相 显示英文标题

标题： Crystalline-equivalent topological phases of many-body fermionic systems in one dimension

摘要： 我们探讨由晶体等价原理相关的二维费米子对称性保护拓扑（SPT）相。 特别是，我们研究分别由手征对称性和反射对称性保护的电荷守恒的多体拓扑相。 虽然这两种晶体等价的SPT相的分类是相同的，但它们的拓扑性质和相结构可能非常不同，这取决于微观细节。 具体而言，我们考虑某些扩展的Su-Schrieffer-Heeger模型，包括有相互作用和无相互作用的情况，这些模型保持手征对称性和反射对称性，并基于系统的基态显式计算多体拓扑不变量。 这些拓扑不变量确定的相结构与模型之间的变形的多体谱完全一致。 正如预期的那样，只有当所有拓扑不变量保持不变时，才存在无能隙的变形。 此外，我们表明可分解系统——那些可以分解为局部且解耦的子系统——可以通过直接与对称性相关的实空间量子数进行拓扑表征。 对于反射对称系统，这些量子数通过体中心对应关系与多体拓扑不变量相关，这种对应关系可以通过广义同调理论中的Atiyah-Hirzebruch谱序列来证明。 最后，我们讨论了过渡对称性在这些SPT相的多体拓扑中的作用。 显示英文摘要

摘要： We explore one-dimensional fermionic symmetry-protected topological (SPT) phases related by the crystalline equivalence principle. In particular, we study charge-conserving many-body topological phases of fermions protected respectively by chiral and reflection symmetries. While the classifications of the two crystalline-equivalent SPT phases are identical, their topological properties and phase structures can be very different, depending on the microscopic details. Specifically, we consider certain extensions of the Su-Schrieffer-Heeger model, with and without interactions, that preserve both chiral and reflection symmetries, and explicitly compute the many-body topological invariants based on the systems' ground states. The phase structures determined by these topological invariants align perfectly with the many-body spectra of deformations among the models. As expected, gapped deformations exist only when all the topological invariants remain unchanged. Moreover, we show that decomposable systems -- those that can be decomposed into local and decoupled subsystems -- can be topologically characterized by real-space quantum numbers directly associated with the symmetries. For reflection-symmetric systems, these quantum numbers are related to the many-body topological invariants via a bulk-center correspondence, which can be justified using the Atiyah-Hirzebruch spectral sequence in generalized homology theory. Finally, we discuss the role of transition symmetry in the many-body topologies of these SPT phases.