超对称保护相的缺陷和简并
Defects and degeneracies in supersymmetry protected phases
摘要：
我们分析了一类一维晶格模型，被称为M $_k$模型，其特征在于顺序$k$集群的自旋费米子和${\cal N}=2$晶格超对称性。我们的主要结果是一类（散装或边缘）的缺陷，这是在一个相应的$\mathbb{Z}_k$ parafermion CFT与所谓的自旋场一一对应的识别。在带隙区，注入这样的缺陷导致基态简并，由超对称性保护。这些缺陷与费米Read-Rezayi量子Hall态上的准空穴非常相似，表现出特征的熔合规则，对于$k=2$，它们属于Ising型;对于$k=3$，它们属于Fibonacci型.
英文摘要：
We analyse a class of 1D lattice models, known as M$_k$ models, which are characterised by an order-$k$ clustering of spin-less fermions and by ${\cal N}=2$ lattice supersymmetry. Our main result is the identification of a class of (bulk or edge) defects, that are in one-to-one correspondence with so-called spin fields in a corresponding $\mathbb{Z}_k$ parafermion CFT. In the gapped regime, injecting such defects leads to ground state degeneracies that are protected by the supersymmetry. The defects, which are closely analogous to quasi-holes over the fermionic Read-Rezayi quantum Hall states, display characteristic fusion rules, which are of Ising type for $k=2$ and of Fibonacci type for $k=3$.
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