  It is well known that symmetry protected topological (SPT) phases host
non-trivial boundaries that cannot be mimicked in a lower-dimensional system
with a conventional realization of symmetry. However, for SPT phases of bosons
(fermions) within the cohomology (supercohomology) classification the boundary
can be recreated without the bulk at the cost of a non-onsite symmetry action.
This raises the question: can one also mimic the boundaries of SPT phases which
lie outside the (super)cohomology classification? In this paper, we study this
question in the context of 2+1D fermion SPTs. We focus on the root SPT phase
for the symmetry group $G =Z_2 \times Z^f_2$. Starting with an exactly solvable
model for the bulk of this phase constructed by Tarantino and Fidkowski, we
derive an effective 1d lattice model for the boundary. Crucially, the Hilbert
space of this 1d model does not have a local tensor product structure, but
rather is obtained by placing a local constraint on a local tensor product
Hilbert space. We derive the action of the $Z_2$ symmetry on this Hilbert space
and find a simple 3-site Hamiltonian that respects this symmetry. We study this
Hamiltonian numerically using exact diagonalization and DMRG and find strong
evidence that it realizes an Ising CFT where the $Z_2$ symmetry acts as the
Kramers-Wannier duality; this is the expected stable gapless boundary state of
the present SPT. A simple modification of our construction realizes the
boundary of the 2+1D topological superconductor protected by time-reversal
symmetry ${\cal T}$ with ${\cal T}^2 = (-1)^{\cal F}$.

Strongly Correlated Electrons