ar X iv : q ua nt - p h / 04 05 06 7 v 1 13 M ay 2 00 4 Entanglement and quantum phase transition in the extended Hubbard model

Quantum entanglement, as one of the most intriguing feature of quantum theory, has been a subject of much studies in recent years, mostly because its nonlocal connotation[1] is regarded as a valuable resource in quantum communication and information processing [2, 3]. One important issue is whether there exists any relation between quantum entanglement and quantum phase transitions [4]. Several groups investigated this problem by study quantum spin systems [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. For example, the work of Osterloh et al.[8] and Osborne and Nielsen[9] on the spin model showed that the entanglement of two neighboring sites displays a sharp peak either near or at the critical point where quantum phase transition undergoes. On the other hand, real systems consist of moving electrons with spin so to explore the relation between quantum entanglement and quantum phase transition in fermionic system is necessary. Previously, there are couple of works studied entanglement in fermionic lattices [15, 16], but they did not discuss its relation to quantum phase transition. In this Letter, in the framework of one-dimensional extended Hubbard model, we study the change of symmetry in the ground state on passing the phase boundary from the point view of quantum entanglement, and demonstrate that entanglement is an unique quantity to describe quantum phase transitions in this system. The one-dimensional extended Hubbard model (EHM) is defined by the Hamiltonian