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arXiv · 1708.05916

Time-dependent topological systems: A study of the Bott index

Daniele Toniolo
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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.

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Daniele Toniolo. 2018-11-27. Time-dependent topological systems: A study of the Bott index. https://doi.org/10.1103/physrevb.98.235425

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