On Z(2)-indices for ground states of fermionic chains
Bourne C, Schulz-Baldes H (2020)
Publication Type: Journal article, Review article
Publication year: 2020
Journal
Book Volume: 32
Journal Issue: 9
DOI: 10.1142/S0129055X20500282
Abstract
For parity-conserving fermionic chains, we review how to associate 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 Z(2)-valued spectral flow provides a topological obstruction for two systems to have the same Z(2)-index. A rudimentary definition of a 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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APA:
Bourne, C., & Schulz-Baldes, H. (2020). On Z(2)-indices for ground states of fermionic chains. Reviews in Mathematical Physics, 32(9). https://dx.doi.org/10.1142/S0129055X20500282
MLA:
Bourne, Chris, and Hermann Schulz-Baldes. "On Z(2)-indices for ground states of fermionic chains." Reviews in Mathematical Physics 32.9 (2020).
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