Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions

Abstract

Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by ${\mathbb{Z}}_4\times {\mathbb{Z}}_2^T$ symmetry. We model the edge Hilbert space by replacing the internal ${\mathbb{Z}}_4$ symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component Luttinger liquid, with nontrivial symmetry transformations that can only be realized in strongly interacting systems. We further demonstrate the symmetry-protected gaplessness under various perturbations, and the bulk-edge correspondence in the theory.

arXiv comment12 pages, 3 figures. Updated; corrected typo in eq 75 of previous version

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