Excited-state level crossing and quantum phase transition in one-dimensional correlated fermion models

We show that for a wide class of one-dimensional correlated fermion models, such as the extended Hubbard model, the global ground state is nondegenerate with proper boundary conditions. Consequently, energy level crossing in the ground state is absent. We also show that the continuous quantum phase transitions are actually caused by level crossing of the low-lying excited states of the system.