Homotopy of periodic two by two matrices
Mathematical Physics
2024-02-21 v3 math.MP
Abstract
We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell.
Cite
@article{arxiv.2212.07529,
title = {Homotopy of periodic two by two matrices},
author = {Joseph E. Avron and Ari M. Turner},
journal= {arXiv preprint arXiv:2212.07529},
year = {2024}
}
Comments
23 pages 12 figures