title: Dimensional Hierarchy of Fermionic Interacting Topological Phases.
abstract: We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Z_{n}.
authors.affiliation: Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany.
authors.forename: Raquel
authors.initials: R
authors.lastname: Queiroz
authors.affiliation: Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany.
authors.forename: Eslam
authors.initials: E
authors.lastname: Khalaf
authors.affiliation: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Ady
authors.initials: A
authors.lastname: Stern