论文标题
$ \ mathbb {z} _2 $拓扑订购状态的弱对称性破坏翻译的理论及其与精确晶格$ \ mathbb {z} _2 $ charuse-flux附件与拓扑超导性的关系
Theory of weak symmetry breaking of translations in $\mathbb{Z}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice $\mathbb{Z}_2$ charge-flux attachment
论文作者
论文摘要
我们通过采用最近开发的2D持续化方法来研究$ \ mathbb {z} _2 $拓扑订购的状态，该状态通过翻译对称性富含对称性，该方法在lattice中实现了精确的$ \ mathbb {z} _2 $ charding-cardus-flux附件。这样的状态可以显示翻译的“弱对称性破裂”，其中哈密顿量和基态都保持完全的不变性，但其对称性被其Anyon Quasi粒子“破碎”，其作用将它们映射到其他超级选择扇区中。 We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of 1D Kitaev wires, leading to the amusing property that there is no local operator that can transport the $π$-flux quasi-particle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant.我们解释了为什么这种现象与其他先前确定的特殊特征（例如基态变性依赖于圆环大小）以及在某些$ \ mathbb {z} _2 _2 _2 $拓扑秩序的状态中的出现。此外，通过将$ \ mathbb {z} _2 $ Charge-flux附件扩展到打开的晶格和气缸，我们构造了一个精确可解决的模型，提供了对其分散性Majorana Gapless边界模式的精确描述。我们还回顾了$ \ MATHBB {Z} \ TIME（\ MATHBB {Z} _2）^3 $ 2D BDG HAMILTONIAN（D类）的分类（D类）具有翻译对称性的富集，并就其互动和自动化障碍的强大稳定性提供了争论，以保留转化的交换。
We study $\mathbb{Z}_2$ topologically ordered states enriched by translational symmetry by employing a recently developed 2D bosonization approach that implements an exact $\mathbb{Z}_2$ charge-flux attachment in the lattice. Such states can display `weak symmetry breaking' of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is `broken' by its anyon quasi-particles, in the sense that its action maps them into a different super-selection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of 1D Kitaev wires, leading to the amusing property that there is no local operator that can transport the $π$-flux quasi-particle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand-in-hand with other previously identified peculiar features such as ground state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain $\mathbb{Z}_2$ topologically ordered states. Moreover, by extending the $\mathbb{Z}_2$ charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the $\mathbb{Z}\times (\mathbb{Z}_2)^3$ classification of 2D BdG Hamiltonians (Class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserves translational symmetry.
