We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant depth local quantum circuits, to a group cohomology theory tensored with lower dimensional cohomology models that depend on the manifold $M$. We comment on the space-time topological quantum field theory (TQFT) interpretation of this result. We also investigate the GDS in the presence of time reversal symmetry, showing that it forms a non-trivial symmetry enriched toric code phase in odd spatial dimensions.

中文翻译：

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解开广义双语义模型

我们从格子哈密顿量的角度分析任意维度的广义双半子 (GDS) 模型类。我们表明，在 $d$ 维空间流形 $M$ 上，GDS 的对偶等效于直到恒定深度的局部量子电路，与依赖于流形 $M$ 的低维上同调模型张量的群上同调理论是等价的. 我们评论了这一结果的时空拓扑量子场论 (TQFT) 解释。我们还研究了存在时间反转对称性的 GDS，表明它在奇数空间维度中形成了一个非平凡的对称性丰富的复曲面码相。