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arXiv · 1905.11556

On $\mathbb{Z}_2$-indices for ground states of fermionic chains

Chris Bourne·Hermann Schulz-Baldes
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Abstract

For parity-conserving fermionic chains, we review how to associate $\mathbb{Z}_2$-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on the infinite CAR algebra. It is shown that the $\mathbb{Z}_2$-valued spectral flow provides a topological obstruction for two systems to have the same $\mathbb{Z}_2$-index. A rudimentary definition of a $\mathbb{Z}_2$-phase label for a class of parity-invariant and pure ground states of the one-dimensional infinite CAR algebra is also provided. Ground states with differing phase labels cannot be connected without a closing of the spectral gap of the infinite GNS Hamiltonian.

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Chris Bourne, Hermann Schulz-Baldes. 2020-02-14. On $\mathbb{Z}_2$-indices for ground states of fermionic chains. https://doi.org/10.1142/s0129055x20500282

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