Year: 2024
Type: article
Abstract: We compare two approaches which use K-theory for C*-algebras to classify symmetry protected topological phases of quantum systems described in the one particle approximation. In the approach by Kellendonk, which is more abstract and more general, the algebra remains unspecified and the symmetries are defined using gradings and real structures. In the approach by Alldridge et al., the algebra is physically motivated and the symmetries implemented by generators which commute with the Hamiltonian. Both approaches use van Daele’s version of K-theory. We show that the second approach is a special case of the first one. We highlight the role played by two of the symmetries: charge conservation and spin rotation symmetry.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0197127
Author: Lorenzo Scaglione
Institutions: Lyon 1 Université, Institut Camille Jordan
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4401633844