论文标题
Chern-Simons拓扑不变的量子和L型量子系统的拓扑不变性
Quantization of Chern-Simons topological invariants for H-type and L-type quantum systems
论文作者
论文摘要
In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance $κ_{xy}=c \frac{π^2 k_B^2}{3h}T$, where the dimensionless $c$ is called chiral central charge.如果有$ u_1 $对称性，则间隙量子阶段也可以具有霍尔电导$σ_{xy} =ν\ frac {e^2} {h} {h} $，其中无量音$ν$称为填充分数。在本文中，我们通过COBORDISM方法来定义Chern-Simons拓扑结构，这些方法与$ C $和$ c $和$ν$相关。特别是，我们获得了依赖于riemannian表面的基态变性的量化条件，以及取决于拓扑分区函数非零的时空歧管类型的量化条件。
In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance $κ_{xy}=c \frac{π^2 k_B^2}{3h}T$, where the dimensionless $c$ is called chiral central charge. If there is a $U_1$ symmetry, a gapped quantum phase can also have a Hall conductance $σ_{xy}=ν\frac{e^2}{h}$, where the dimensionless $ν$ is called filling fraction. In this paper, we derive some quantization conditions of $c$ and $ν$, via a cobordism approach to define Chern--Simons topological invariants which are associated with $c$ and $ν$. In particular, we obtain quantization conditions that depend on the ground state degeneracies on Riemannian surfaces, and quantization conditions that depend on the type of spacetime manifolds where the topological partition function is non-zero.
