论文标题
混合级别-1和等级-2 U（1）晶格量规理论，F3模型及其有效的场理论
Hybrid rank-1 and rank-2 U(1) lattice gauge theory, the F3 model, and its effective field theory
论文作者
论文摘要
通过“ higgsing”的数学过程，许多确切的可解决的自旋模型，包括两个维度和三个维度的Kitaev旋转代码以及三个维度的X-Cube模型，都与其各自的父晶格理论（LGT）有关。这些自旋模型的低能激发的现场理论可以随后建立在母体LGT的对称性上。最近，目前的两位作者提出了三维曲折代码的变体，我们现在称之为F3模型，其基本激发由X-Cube模型的三维曲曲面代码和分裂式激发的Freeon和Fluxon激发组成。在这项工作中，我们将F3模型的母体LGT确定为混合级别-1和Rank-2 U（1）LGT，并开发相应的场理论。 F3模型的生成的Lagrangian是带有额外术语的三维复曲面代码的拉格朗日，该代码将分布量的动力学与磁通量联系起来。通过仔细跟踪F3模型的规格不变性，也可以得出有效动作的物质部分。流体动力学方程是衍生的，这是正确反映其受约束动力学的。最后，我们为F3模型中的准粒子运动提供了一个紧密结合模型。
A number of exactly solvable spin models, including the Kitaev toric code in two and three dimensions and the X-cube model in three dimensions, can be related to their respective parent lattice gauge theories (LGT) through the mathematical process of 'Higgsing'. Field theories of the low-energy excitations of these spin models can be developed subsequently, building upon the symmetry of the parent LGTs. Recently, two of the present authors proposed a variant of the three-dimensional toric code which we now call the F3 model, whose elementary excitations consist of freeon and fluxon excitations of the three-dimensional toric code and fracton excitations of the X-cube model. In this work, we identify the parent LGT of the F3 model as the hybrid rank-1 and rank-2 U(1) LGT, and develop the corresponding field theory. The resulting Lagrangian of the F3 model is that of a three-dimensional toric code with an extra term, which ties the dynamics of fractons to that of fluxons. The matter part of the effective action for the F3 model can be derived as well, by carefully keeping track of the gauge invariance of the F3 model. Hydrodynamic equations of motion of the quasiparticles are derived, which properly reflect their constrained dynamics. Finally, we present a tight-binding model for the quasiparticle motion in the F3 model.
