Hannover 2016 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 10: Quantum Optics II
Q 10.1: Vortrag
Montag, 29. Februar 2016, 14:30–14:45, f442
Topological classification of one-dimensional symmetric quantum walks — •Christopher Cedzich1, Tobias Geib1, Francisco Alberto Grünbaum2, Christoph Stahl1, Luis Velazquez3, Albert Werner4, and Reinhard Werner1 — 1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany — 2Department of Mathematics, University of California, Berkeley CA 94720 — 3Departamento de Matematica Aplicada & IUMA, Universidad de Zaragoza, Maria de Luna 3, 50018 Zaragoza, Spain — 4Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
We study symmetry protected topological phases for one-dimensional quantum walks. Topological phases play an important role in the classification of quantum matter. An analogous phase classification of quantum walks encounters the problem that walks are given by a unitary operator rather than a Hamiltonian. As a consequence, walks allow local perturbations which cannot be continuously contracted to the identity without violating unitarity, symmetry or a gap condition. This leads to an additional invariant in the homotopy classification which is, however, not invariant under local but not contractible perturbations.
(See also the related talk by T. Geib)