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

Abstract

The Mott-Hubbard transition is studied in the context of thetwo-dimensional Hubbard model. Analytical calculations show theexistence of a critical value Uc of the potential strength whichseparates a paramagnetic metallic phase from a paramagnetic insulatingphase. Calculations of the density of states and double occupancy showthat the ground state in the insulating phase contains always a smallfraction of empty and doubly occupied sites. The structure of theground state is studied by considering the probability amplitude ofintersite hopping. The results indicate that the ground state of theMott insulator is characterized by a local antiferromagnetic order; theelectrons keep some mobility, but this mobility must be compatible withthe local ordering. The vanishing of some intersite probabilityamplitudes at U = Uc puts a constraint on the electron mobility. Itis suggested that such quantities might be taken as the quantitieswhich control the order in the insulating phase.