标题： 从高阶贝里相位的角度看共形边界条件的空间：参数化BCFT中的贝里曲率流 显示英文标题

标题： Space of conformal boundary conditions from the view of higher Berry phase: Flow of Berry curvature in parametrized BCFTs

摘要： 在本工作中，我们研究两个主题之间的联系：边界共形场理论（BCFTs）中的共形边界条件空间与由更高贝里相位表征的体系统空间。 我们通过分析带有连续参数化共形边界条件的狄拉克费米子BCFT中的多参数谱流来探索这一联系，这些边界条件是通过将共形场理论（CFT）耦合到一族体系统引入的。 当体系统属于非平凡的更高贝里类时，相关的共形边界条件会引发普通贝里曲率的流动，在BCFT的福克空间中产生陈数泵。 这一现象是单维参数化体系统中贝里曲率流动的BCFT对应物，其中流动发生在实空间中。 基于这种对应关系，我们在BCFT框架内引入了更高贝里曲率和更高贝里不变量的概念。 我们的结果为研究共形边界态和体基态族的拓扑性质提供了新的视角：如果一族体态属于非平凡的更高贝里类，则相应的纠缠哈密顿量表现出携带贝里曲率的多参数谱流。 显示英文摘要

摘要： In this work, we study the connection between two subjects: the space of conformal boundary conditions in boundary conformal field theories (BCFTs) and the space of gapped systems characterized by higher Berry phases. We explore this connection by analyzing multi-parameter spectral flow in Dirac fermion BCFTs with continuously parametrized conformal boundary conditions, which are introduced by coupling a CFT to a family of gapped systems. When the gapped systems belong to a nontrivial higher Berry class, the associated conformal boundary conditions induce a flow of the ordinary Berry curvature, resulting in a Chern number pump in the Fock space of the BCFT. This phenomenon is the BCFT analog of Berry curvature flow in one-dimensional parametrized gapped systems, where the flow occurs in real space. Building on this correspondence, we introduce the notions of higher Berry curvature and higher Berry invariants within the BCFT framework. Our results provide a new perspective for studying the topological properties of families of conformal boundary states and gapped ground states: if a family of gapped states belongs to a nontrivial higher Berry class, then the corresponding entanglement Hamiltonians exhibit a multi-parameter spectral flow that carries Berry curvature in the Fock space.