论文标题
在二维可溶解的旋转液体中的有效分形行为
Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
论文作者
论文摘要
在这项工作中，我们提出了一个$ \ mathbb {z} _n $时钟模型，该模型可在晶格上解决。我们发现低能物理学的外来特性，例如UV/IR混合和具有限制迁移率的激发，它们类似于来自较高维模型的分化物理。然后，我们在两个不同的方案中研究了晶格系统的连续描述，并为每个制度找到了两种定性不同的领域理论。特征时间尺度以$ n^2 $呈指数级增长的特征时间尺度（随着系统参数的函数迅速分化）将这两个制度分开。在低于此量表的时间，该系统由有效的分数类似于类似的分子样作用来描述，在该动作中，更高形式的对称性阻止了绝望。在这个制度中，该系统作为孤立的粒子有效地表现为分裂，实际上，它永远不会离开其原始位置。除了较大的特征时间尺度之外，激发是移动的，有效的场理论是由纯粹的互惠simons动作给出的。在此制度中，系统的UV/IR属性是由翻译组的特殊实现捕获的。
In this work we propose a $\mathbb{Z}_N$ clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with $N^2$ (and diverges rapidly as a function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hoping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system are captured by a peculiar realization of the translation group.
