论文标题
梯子上的离散的亚伯晶格量规及其二元性用量子钟型号
Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
论文作者
论文摘要
我们研究了从$ \ mathbb {z} _n $ lattice量规理论的量规不变子空间上的二元性转换，到单链上的$ n $ clock模型。该映射的主要特征是时钟模型中纵向场的出现，其值取决于量规模型的超选择性扇区，这意味着规格理论的不同扇区可以显示完全不同的相图。为了调查这一点并查看限制阶段是否可能出现，我们使用精确的对角线化和DMRG对$ n = 2、3、4 $进行数值分析。
We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model, implying that the different sectors of the gauge theory can show quite different phase diagrams. In order to investigate this and see if confined phases might emerge, we perform a numerical analysis for $N = 2, 3, 4$, using exact diagonalization and DMRG.
