Homotopy of periodic two by two matrices
arXiv (Cornell University)(2022)
Abstract
We describe the homotopy classes of $2\times 2$ 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.
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Key words
matrices
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