论文标题
$ \ mathbb {z} _n $ toric代码的家族中的圆环的基态变性
Ground state degeneracy on torus in a family of $\mathbb{Z}_N$ toric code
论文作者
论文摘要
$ 2+1 $尺寸的拓扑排序通常以三个相关特征为特征：分数化（任何）激发，拓扑纠缠熵和强大的基态退化，不需要对称性保护或自发对称性。这种堕落性被称为拓扑变性，通常在周期性边界条件下可以看到，无论系统尺寸$ l_1 $和$ l_2 $在每个方向上的选择如何。在这项工作中，我们将Kitaev Etric代码的扩展名介绍给$ N $ Level Spins（$ n \ geq2 $）。该模型根据模型中的参数实现了拓扑排序的阶段或受对称保护的拓扑阶段。拓扑排序的阶段的最显着特征是，尽管型号的翻译对称性仍然没有破裂，但取决于$ l_1 $和$ l_2 $的基态可能是唯一的。尽管如此，拓扑纠缠熵具有非平凡的价值。我们认为，这种行为源于翻译的非平凡作用。
Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not require symmetry protection or spontaneous symmetry breaking. Such degeneracy is known as topological degeneracy and usually can be seen under the periodic boundary condition regardless of the choice of the system size $L_1$ and $L_2$ in each direction. In this work we introduce a family of extensions of the Kitaev toric code to $N$ level spins ($N\geq2$). The model realizes topologically ordered phases or symmetry-protected topological phases depending on parameters in the model. The most remarkable feature of the topologically ordered phases is that the ground state may be unique, depending on $L_1$ and $L_2$, despite that the translation symmetry of the model remains unbroken. Nonetheless, the topological entanglement entropy takes the nontrivial value. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.
