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

The Mott-Hubbard transition is studied in the context of the two-dimensiona l Hubbard model. Analytical calculations show the existence of a critical v alue 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 ph ase contains always a small fraction of empty and doubly occupied sites. Th e structure of the ground state is studied by considering the probability a mplitude of intersite hopping. The results indicate that the ground state o f the Mott insulator is characterized by a local antiferromagnetic order; t he electrons keep same mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U = U-c puts a constraint on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order i n the insulating phase.