格点Clifford分形子及其类Chern-Simons理论
Lattice Clifford fractons and their Chern-Simons-like theory
摘要：
我们使用Clifford代数的Dirac矩阵表示来建立格点上的分形子模型及其有效的Chern-Simons类理论。作为一个例子，我们建立了奇数$D$空间维的格点分形及其$(D+1)$有效理论。该模型具有反对称的$K$矩阵类似的分级量子霍尔态。规范荷在子维流形中是守恒的，这保证了分形行为。该结构扩展到任何晶格分形模型建立从交换投影仪和张量产品的自旋$1/2$自由度的网站。
英文摘要：
We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.
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