2017/08/31 by Daniele Toniolo · 1 citation
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.quant-gas
paper · pdf · doi:10.1103/physrevb.98.235425
published as Phys. Rev. B 98, 235425 (2018) · 8 pages, partial rephrasing of title and sections' title. Partial rewriting of the introduction. Results unchanged. Accepted by PRB
arxiv created 2018/11/27 · arxiv updated 2019/01/08
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.