Quantum order: a quantum entanglement of many particles

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum orders in free fermion systems and in 2D spin-1/2 systems. We generalize the Landau's theory for the classical orders and introduce projective symmetry group and Fermi surface topology to characterize different quantum orders. (C) 2002 Elsevier Science B.V. All rights reserved.