论文标题
带有子系统对称性的玻色子弗屈服二元性
Boson-fermion duality with subsystem symmetry
论文作者
论文摘要
我们探索了$（2+1）$ d的确切双重性，这是在具有$ \ mathbb {z} _2 $子系统对称性的波斯型理论的费米化和带有$ \ mathbb {z} _2 $ Subsystem SupSystem Fermion fermion parity Parity Symettry Symmetry的Fermionic Themore之间。一个典型的例子是Plaquette Ising模型的费米化与Plaquette Fermion模型之间的二元性。我们首先在$（1+1）$ d中重新访问标准玻色子 - 弗米恩二元性，并使用$ \ mathbb {z} _2 $ 0- $ 0-FROM对称性，以可推广到$（2+1）$ d的方式表示。我们使用$ \ Mathbb {z} _2 $子系统对称性进行$（2+1）$ D，并通过使用广义的Jordan-Wigner地图在晶格上建立确切的双重性，并仔细讨论了扭曲和对称扇区的映射。这促使我们引入了表现出叶面结构的子系统ARF不变性。
We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a $\mathbb{Z}_2$ subsystem symmetry and a fermionic theory with a $\mathbb{Z}_2$ subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. We first revisit the standard boson-fermion duality in $(1+1)$d with a $\mathbb{Z}_2$ 0-from symmetry, presenting in a way generalizable to $(2+1)$d. We proceed to $(2+1)$d with a $\mathbb{Z}_2$ subsystem symmetry and establish the exact duality on the lattice by using the generalized Jordan-Wigner map, with a careful discussion on the mapping of the twist and symmetry sectors. This motivates us to introduce the subsystem Arf invariant, which exhibits a foliation structure.
