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https://doi.org/10.1142/S0129055X20500282Cited by:7 (Source: Crossref)

For parity-conserving fermionic chains, we review how to associate 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 2-valued spectral flow provides a topological obstruction for two systems to have the same 2-index. A rudimentary definition of a 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.

AMSC: 81T75, 81V70, 58J30

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