TKNN formula for general lattice Hamiltonian in odd dimensions
Abstract
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 non-minimal 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.
Cite
@article{arxiv.2003.08076,
title = {TKNN formula for general lattice Hamiltonian in odd dimensions},
author = {Hidenori Fukaya and Tetsuya Onogi and Satoshi Yamaguchi and Xi Wu},
journal= {arXiv preprint arXiv:2003.08076},
year = {2020}
}
Comments
talk presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China. Based on arXiv:1903.11852