  Strong interactions can give rise to new fermionic symmetry protected
topological phases which have no analogs in free fermion systems. As an
example, we have systematically studied a spinless fermion model with $U(1)$
charge conservation and time reversal symmetry on a three-leg ladder using
density-matrix renormalization group. In the non-interacting limit, there are
no topological phases. Turning on interactions, we found two gapped phases. One
is trivial and is adiabatically connected to a band insulator, while another
one is a nontrivial symmetry protected topological phase resulting from strong
interactions.
