Physical Review Letters ( IF 8.385 ) Pub Date : 2021-01-13 , DOI: 10.1103/physrevlett.126.021603
Michael DeMarco; Xiao-Gang Wen

We propose a bosonic ${\mathrm{U}}^{\kappa }\left(1\right)$ rotor model on a three dimensional spacetime lattice. With the inclusion of a Maxwell term, we show that the low-energy properties of our model can be obtained reliably via a semiclassical approach. Those properties are the same as that of the Chern-Simons field theory, $S=\int {d}^{3}x\left({K}_{IJ}/4\pi \right){A}_{I}d{A}_{J}$. We require the lattice variables on each link to be compact (i.e., take values on circles), which enforces the quantization of the $K$ matrix as a symmetric integer matrix with even diagonals. Our lattice model also has exact 1-symmetries, which gives rise to the 1-form symmetry in the Chern-Simons field theory. In particular, some of those 1-symmetries are anomalous (i.e., non-on-site) in the expected way. The anomaly can be probed via the breaking of those lattice 1-symmetries by the boundaries.

CompactUk（1）Chern-Simons理论作为具有精确离散1对称性的局部Bosonic晶格模型

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