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-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc 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 U = Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase. There are several indications that the two-dimensional Hubbard model (HM) can describe a metal-insulator transition and that some kind of order is established in the paramagnetic insulating state. However, there is no clear picture about the structure of the ground state and no indication about the existence of an order parameter. In particular, there is a difficulty to conciliate the existence of a finite value for the doubly occupancy, which implies mobility of the electrons, and the existence of some order which would imply a localization of the electrons. In this article we study the Hubbard model by means of the composite operator method (COM) in the two-pole approximation. The main results can be so summarized: (i) a MottHubbard transition does exist; (ii) a local antiferromagnetic (AF) order is present in the insulating state; (iii) a quantity which controls the order in the insulating state is individuated. () E-mail: [email protected] Typeset using EURO-TEX 2 EUROPHYSICS LETTERS According to the band model approximation several transition oxides should be metals. In practice one finds both metallic and insulating states, with a metal-insulator transition induced by varying the boundary conditions (pressure, temperature, compound composition). Mott [1] pointed out that for narrow bands the electrons are localized on the lattice ions and therefore the correlations among them cannot be neglected. A model to describe these correlations was proposed by Hubbard [2]. In a standard notation his Hamiltonian is given by