论文标题
ISING Code BiLayer中两个拓扑排序相之间的量子临界相变
Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
论文作者
论文摘要
我们证明了正方形晶格上的两个曲折代码层结合通过ISING相互作用显示两个具有内在拓扑顺序的不同阶段。 The second-order quantum phase transition between the weakly-coupled $\mathbb{Z}_2\times\mathbb{Z}_2$ and the strongly-coupled $\mathbb{Z}_2$ topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the 3d Ising$^*$ universality class.这可以通过对方格上的横向视野模型的精确二元性转换来显示，该模型基于大量本地$ \ mathbb {z} _2 $保守的平族的存在。这些保守的数量对应于不同层上两个相邻恒星操作员的乘积。值得注意的是，我们表明，涉及大iSing耦合极限的低能量有效模型由有效的单层复合代码根据ising toric code biilayer的保守量给出。这两个拓扑阶段的进一步特征是拓扑纠缠熵，该介于非本地阶参数。
We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled $\mathbb{Z}_2\times\mathbb{Z}_2$ and the strongly-coupled $\mathbb{Z}_2$ topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the 3d Ising$^*$ universality class. This can be shown by an exact duality transformation to the transverse-field Ising model on the square lattice, which builds on the existence of an extensive number of local $\mathbb{Z}_2$ conserved parities. These conserved quantities correspond to the product of two adjacent star operators on different layers. Notably, we show that the low-energy effective model derived about the limit of large Ising coupling is given by an effective single-layer toric code in terms of the conserved quantities of the Ising toric code bilayer. The two topological phases are further characterized by the topological entanglement entropy which serves as a non-local order parameter.
