Thouless-Kohmoto-Nightingale-den Nijs formula for a general Hamiltonian
Thouless-Kohmoto-Nightingale-den Nijs formula for a general Hamiltonian
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一般哈密顿量的 Thouless-Kohmoto-Nightingale-den Nijs 公式
DOI：
10.1103/physrevd.101.074507
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发表时间：
2020
影响因子：
5
通讯作者：
Wu Xi
中科院分区：
文献类型：
--
作者：
Fukaya Hidenori;Onogi Tetsuya;Yamaguchi Satoshi;Wu Xi
奇数维的拓扑绝缘体由拓扑数来表征。我们通过显式计算证明了贝里曲率的陈省身特征给出的拓扑数与费米子中一般类双线性哈密顿量的低能有效作用的陈省身-西蒙斯能级之间的众所周知的关系，具有一般 U(1) 规范相互作用，包括非最小耦合。一系列 Ward-Takahashi 恒等式对于将 Chern-Simons 能级与绕数联系起来至关重要，然后可以通过对时间动量进行积分，将其直接简化为贝里曲率的 Chern 特征。
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including nonminimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.