Integer-filling metal-insulator transitions in the degenerate Hubbard model

Abstract

We obtain exact numerical solutions of the degenerate Hubbard model in the limit of large dimensions (or large lattice connectivity). Successive Mott-Hubbard metal insulator transitions at integer fillings occur at intermediate values of the interaction and low enough temperature in the paramagnetic phase. The results are relevant for transition metal oxides with partially filled narrow degenerate bands. 71.27.+a, 71.30.+h, 71.20.Ad The understanding of strongly correlated electron systems is one of the current challenges in condensed matter physics. In recent years, this problem has received a great deal of attention from theorists and experimentalist alike. Yet, our knowledge of even some of the basic features of the proposed model Hamiltonians remains to a large extent only partial, except, perhaps, in the onedimensional case. In consequence, the interpretation of the experimental data of strongly correlated electron systems has to remain only speculative in most of the cases. In regard of this situation, exact results on properties of model Hamiltonians in well defined limits is very desirable. The relevant role played by the band degeneracy in models of strongly correlated electrons has been long and largely recognized [1][2][3][4]. However, the systematic treatment of such models poses in general even greater technical difficulties than non-degenerate ones. This particularly applies to numerical approaches which have to deal with the exponential grow of the Hilbert space.The goal of this paper is to demonstrate the existence of successive metal insulator transitions (MIT) at the integer fillings n = 1, 2, 3 in the two band degenerate Hubbard model within the "Local impurity self-consistent approximation" (LISA) [5] which is exact in the limit of large dimensions (or large lattice connectivity) [6]. These MIT occur within the paramagnetic phase for intermediate values of the interaction. We obtain exact numerical solutions of the model using an extension of the Hirsch and Fye quantum Monte Carlo (HFQMC) algorithm [7,8] for the solution of the associated impurity problem within the LISA. This impurity problem is a generalized single impurity Anderson model where the impurity and conduction band operators carry an orbital index.The two band degenerate Hubbard model reads,ij labels nearest neighbor sites and a, b = 1, 2 is the orbital index. This Hamiltonian is rotational invariant in spin and real space and the usual approximation U and J independent of band indices is assumed [9]. The parameter U is due to on-site Coulomb repulsion and the exchange parameter J originates the Hund's coupling. For simplicity, we shall further assume t ab ij = −tδ ab and neglect the last "spin flip" term in (1). The resulting model Hamiltonian is relevant for for electronic systems with partially filled narrow degenerate bands. Examples of such systems are the 3d transition metal oxides R 1−x A x M O 3 with three-dimensional perovskitetype structure, where R = La, Y , A = Ca, Sr and the transition metal M = T i, V, Cr. Fujim...

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