  We characterize the Mott insulator and Luther-Emery phases of the 1D Hubbard
model through correlators that measure the parity of spin and charge strings
along the chain. These non-local quantities order in the corresponding gapped
phases and vanish at the critical point $U_c=0$. The Mott insulator consists of
bound doublon-holon pairs, which in the Luther-Emery phase turn into electron
pairs with opposite spins, both unbinding at $U_c$. The behavior of the parity
correlators can be captured by an effective free spinless fermion model.
