论文标题
FCC，Checkerboards，Fracton和QFT
FCC, Checkerboards, Fractons, and QFT
论文作者
论文摘要
我们考虑在FCC晶格上的XY旋转自由度，因此该系统尊重某些子系统全球对称性。然后，我们评估了这个全球对称性，并研究了FCC晶格的相应$ u（1）$量规理论。令人惊讶的是，这个$ u（1）$量规理论对于原始旋转系统是双重的。我们还分析了该晶格上类似的$ \ mathbb {z} _n $ gauge理论。所有这些系统都是分形的。 $ u（1）$理论是无间隙的，并且$ \ mathbb {z} _n $理论被忽略了。我们分析了所有这些系统的连续性限制，并以低能物理学的形式呈现免费的连续lagrangians。 我们的$ \ mathbb {z} _2 $ fcc仪表理论是众所周知的分形棋盘模型的连续限制。我们的连续分析导致了一个直接的证明，即该理论是$ \ mathbb {z} _2 $ x-cuble模型的两个副本的已知事实。 我们发现已知模型之间的新模型和新的关系。 $ \ mathbb {z} _n $ fcc仪表理论可以通过将线条和平面的各向异性模型的三个副本与某些异国情调的$ \ mathbb {z} _2 _2 $仪表理论结合在一起来实现。另外，尽管对于$ n = 2 $，此型号是$ \ mathbb {z} _2 $ x-cuble型号的两个副本双副本，但对于较高的$ n $而言，类似的语句是不正确的。
We consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the FCC lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar $\mathbb{Z}_N$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the $\mathbb{Z}_N$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our $\mathbb{Z}_2$ FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the $\mathbb{Z}_2$ X-cube model. We find new models and new relations between known models. The $\mathbb{Z}_N$ FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic $\mathbb{Z}_2$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the $\mathbb{Z}_2$ X-cube model, a similar statement is not true for higher $N$.
