  We study the two-dimensional (2D) Hubbard model using exact diagonalization
for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a
single hexagon per site. In certain parameter ranges, the Hubbard model maps to
a quantum compass model on those lattices. On the triangular lattice, the
compass model exhibits collinear stripe antiferromagnetism, implying
$d$-density wave charge order in the original Hubbard model. On the honeycomb
lattice, the compass model has a unique, quantum disordered ground state that
transforms nontrivially under lattice reflection. The ground state of the
Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic
symmetry-protected topological phase. This state -- protected by time-reversal
and reflection symmetries -- cannot be connected adiabatically to a
free-fermion topological phase.
