任意子凝聚：相干态、对称性丰富的拓扑相、Goldstone定理和对称性的动力学重排
Anyon Condensation: Coherent states, Symmetry Enriched Topological Phases, Goldstone Theorem, and Dynamical Rearrangement of Symmetry
摘要：
尽管近年来拓扑相中任意子凝聚的数学问题得到了深入的研究，但要证明它的物理存在性，就相当于构造一个有效的哈密顿理论。本文通过建立有效哈密顿量和希尔伯特空间，具体地建立了任意子凝聚的物理基础，其中我们明确地把凝聚相的真空构造为相干态，相干态是生成凝聚任意子的生成算符的本征态。随着这一建设，这是类似于Laughlin的分数量子霍尔态的波函数的建设，我们推广的Goldstone定理在通常的自发对称性破缺范例的情况下的任意子凝聚。通过直接构造相应的对称变换，我们证明了凝聚相是一个对称性丰富的（保护的）拓扑相，这可以看作是Bogoliubov变换的推广.
英文摘要：
Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space, in which we explicitly construct the vacuum of the condensed phase as the coherent states that are the eigenstates of the creation operators that create the condensate anyons. Along with this construction, which is analogous to Laughlin's construction of wavefunctions of fractional quantum hall states, we generalize the Goldstone theorem in the usual spontaneous symmetry breaking paradigm to the case of anyon condensation. We then prove that the condensed phase is a symmetry enriched (protected) topological phase by directly constructing the corresponding symmetry transformations, which can be considered as a generalization of the Bogoliubov transformation.
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