Classification of interacting fermionic phases by dimensional re - duction

Submitted for the MAR16 Meeting of The American Physical Society Classification of interacting fermionic phases by dimensional reduction RAQUEL QUEIROZ, ESLAM KHALAF, Max Planck Institute for Solid State Physics, ADY STERN, Weizmann Institute of Science — Topological phases of noninteracting fermions are classified in each spatial dimension according to their symmetry class, in a periodic way [1]. When including interactions, however, this classification can be modified. It was first shown that in one-dimensional chains, the Z classification of the BDI symmetry class is reduced to Z8 [2]. That is, every group of 8 Majorana states at the edge of a BDI chain can be gapped out through a suitable interaction, despite preserving its fundamental symmetries. In this work, we present a dimensional reduction argument to derive the role of interactions in the classification of fermionic symmetry protected topological phases. For symmetry classes classified by a Z invariant in odd dimensions, we propose a general n-particle quartic interaction that renders the system topologically trivial. We argue that all phases characterized by a topological invariant smaller than n in the noninteracting limit remain topologically distinct once interactions are included, thereby reducing the noninteracting Z classification to Zn. [1] Ryu, S., et. al., NJP 12, 065010 (2010); [2] Fidkowski, L. and Kitaev, A., PRB 81, 134509 (2010). Raquel Queiroz Max Planck Institute for Solid State Physics Date submitted: 06 Nov 2015 Electronic form version 1.4