Non-local order parameters for the 1D Hubbard model
  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. 
Arianna Montorsi and Marco Roncaglia
cond-mat.str-el quant-ph