[seminar] Title: Topological phases of one-dimensional quantum walks
joint work with Christopher Cedzich, Alberto Grünbaum, Chistoph Stahl, Luiz Velazques, Albert H. Werner Symmetry protected topological phases of quantum lattice systems such as free fermion systems are currently a hot topic in the solid state community. Unfortunately, much of this literature is heuristic, and it is hard to find precise statements, let alone proofs. I will study the case of discrete time dynamics, i.e., quantum walks, and provide a straightforward, but fully rigorous treatment, of all five discrete symmetry types, emphasizing the common structures. The discrete time case, in which the object of study is the unitary one-step operator rather than a Hamiltonian has some additional subtleties, notably the existence of local perturbations, which cannot be contracted continuously to the identity in a symmetry respecting way.
- Date: 09 September 2015