Time-dependent topological systems: A study of the Bott index
Abstract
The Bott index is an index that discerns among pairs of unitary matrices that can or cannot be approximated by a pair of commuting unitary matrices. It has been successfully employed to describe the approximate integer quantization of the transverse conductance of a system described by a short-range, bounded and spectrally gapped Hamiltonian on a finite two dimensional lattice on a torus and to describe the invariant of the Bernevig- Hughes-Zhang model even with disorder. This paper shows the constancy in time of the Bott index and the Chern number related to the time-evolved Fermi projection of a thermodynamically large system described by a short-range and time-dependent Hamiltonian that is initially gapped. The general situation of a ramp of a time-dependent perturbation is considered, a section is dedicated to time-periodic perturbations.
Keywords
Cite
@article{arxiv.1708.05916,
title = {Time-dependent topological systems: A study of the Bott index},
author = {Daniele Toniolo},
journal= {arXiv preprint arXiv:1708.05916},
year = {2019}
}
Comments
8 pages, partial rephrasing of title and sections' title. Partial rewriting of the introduction. Results unchanged. Accepted by PRB