Quantization of Chern-Simons topological invariants for H-type and L-type quantum systems

Oscar Randal-Williams, Lokman Tsui, Xiao-Gang Wen

In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance ${\kappa }_{xy}=c\frac{{\pi }^2{k}_B^2}{3h}T$, where the dimensi…