论文标题
在（3+1）d toric代码的张量网络表示上
On tensor network representations of the (3+1)d toric code
论文作者
论文摘要
我们定义了（3+1）d的两个双张量网络表示基态基态子空间。这两种表示最初通过施加稳定器约束的家族而获得的，其特征是分别由字符串样和膜状操作员生成的不同的虚拟对称性。我们从这些虚拟对称性的角度讨论了模型的拓扑特性，强调了两种表示之间的差异。特别是，我们认为，根据表示，边界纠缠自由度的相图自然与（2+1）d hamiltonian显示出显示全局或量规$ \ mathbb z_2 $ symmetraly的相位图。
We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge $\mathbb Z_2$-symmetry.
