H型和L型量子系统Chern-Simons拓扑不变量的量子化
Quantization of Chern-Simons topological invariants for H-type and L-type quantum systems
摘要：
在2+1维（2+1D）中，不具有对称性（即拓扑序）的带隙量子相可以具有热霍尔电导$κ_{xy}=c \frac{π^2 k_B^2}{3h}T$，其中无量纲的$c$被称为手性中心荷。如果存在$U_1$对称性，则带隙量子相也可以具有霍尔电导$σ_{xy}=ν\frac{e^2}{h}$，其中无量纲的$ν$称为填充分数。本文通过协边方法，导出了$c$和$ν$的量子化条件，定义了与$c$和$ν$相关的Chern-Simons拓扑不变量.特别是，我们得到的量子化条件依赖于黎曼曲面上的基态退化，和量子化条件依赖于拓扑配分函数是非零的时空流形的类型。
英文摘要：
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. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
