The Mott-Hubbard transition and the paramagnetic insulating state in the two-dimensional Hubbard model

Dipartimento di Scienze Fisiche “E. R. Caianiello”, Unità INFM di Salerno Università degli Studi di Salerno - 84081 Baronissi, Salerno, Italy

Corresponding author: mancini@vaxsa.csied.unisa.it

Received: 4 January 1999
Accepted: 27 January 2000

Abstract

The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value U_c of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at puts a constraint on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.