量子链上等变拟局部自同构的分类
Classification of equivariant quasi-local automorphisms on quantum chains
摘要：
我们对量子链上的自同构进行分类，允许自旋和费米子自由度，而且相对于有限对称群$G$的局部对称作用是等变的。通过强连续变形和叠加解耦的辅助自同构，分类达到等价。我们发现等价类是唯一的标记的指数采取值在$\mathbb{Q} \cup \sqrt{2} \mathbb{Q} \times \mathrm{Hom}(G, \mathbb{Z}_2) \times H^2(G, U(1))$。讨论了该指数与自旋链上一维对称性保护拓扑相指数的关系，该指数取值于$H^2(G, U(1))$。
英文摘要：
We classify automorphisms on quantum chains, allowing both spin and fermionic degrees of freedom, that are moreover equivariant with respect to a local symmetry action of a finite symmetry group $G$. The classification is up to equivalence through strongly continuous deformation and stacking with decoupled auxiliary automorphisms. We find that the equivalence classes are uniquely labeled by an index taking values in $\mathbb{Q} \cup \sqrt{2} \mathbb{Q} \times \mathrm{Hom}(G, \mathbb{Z}_2) \times H^2(G, U(1))$. We discuss te relation of this index to the index of one-dimensional symmetry protected topological phases on spin chains, which takes values in $H^2(G, U(1))$.
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