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.

中文翻译：

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Lattice Clifford分形及其类Chern-Simons理论

我们使用Clifford代数的Dirac矩阵表示法在晶格及其有效的类似Chern-Simons的理论上建立分形模型。例如，我们以奇数$ D $空间尺寸及其有效理论（$（D + 1）$）构造晶格分数。该模型具有类似于分层量子霍尔状态的反对称$ K $矩阵。标量电荷保存在次维歧管中，以确保分形行为。该构造可扩展到任何由通勤投影仪构建的格子分数维模型，并在现场具有自旋$ 1/2 $自由度的张量产品。