  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.
