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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)