Intrinsically interacting symmetry protected phases of fermions

Interactions can profoundly affect the classification of fermionic symmetry protected topological (SPT) phases. In addition to sometimes collapsing the non-interacting classification, they also enable the existence of entirely new, intrinsically interacting phases, not adiabatically connected to any free fermion topological insulator or superconductor. Beyond the existence of special exactly solved models and an abstract bulk characterization in terms of three loop braiding and cobordism, little is understood about these phases, and in particular about the surface states they admit. In this work, we advance an understanding of the surface states of such intrinsically interacting fermionic SPTs. In particular, we find gapped symmetry preserving topologically ordered surface states, and propose a new ’t Hooft anomaly characterizing such fermionic surfaces, connecting the surface physics to the bulk SPT order.