One-Band Hubbard Model: Definition and Early Solutions

Volodymyr Turkowski

John A. Blackman, D. M. Esterling

Fabian H. L. Eßler, Holger Frahm, Frank Göhmann +2 more

The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands, and which has been applied to problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This 2005 book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.

Hal Tasaki

Jian Ping Lu

Degenerate Hubbard models are studied using the Generalized-Gutzwiller-Approximation. It is found that the metal-insulator transition occurs at a finite correlation Uc when the average number of electrons per lattice site is an integer. The critical Uc depends sensitively on both the band degeneracy N and the filling x. A derivation is presented for the general expression of Uc(x,N) which reproduces all previously known Gutzwiller solutions, including that of the Boson Hubbard model. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed. PACS numbers: 71.10.+x,71.30.+h,74.70.W Typeset using REVTEX 1 The simple Hubbard model, where each lattice site is occupied by at most two electrons, has been extensively studied in recent years as a model of strongly correlated electron systems. 1,2 But in many systems, such as molecular solids C60 and AxC60, 3 the conduction band is degenerate which allows the occupation of more than two electrons per lattice site. For these systems, studying the degenerate Hubbard model on a lattice is the first step toward the understanding of electron-electronic correlations. Yet, there has been little progress since the pioneering works of Chao and Gutzwiller in early 1970s. 4 Recently, we succeeded in obtaining the Gutzwiller-like analytical solutions to degenerate Hubbard models using a scheme similar to the original Gutzwiller-Approximation. 5 A brief report of our results has been published. 6 The solution was used successfully to interpret the unusual metal-insulator transitions observed in fullerides AxC60. 6,7 In this paper we present details of our derivation and the approximation. In addition, effects of the crystal lattice structure on the metal-insulator transition and the effective mass are also investigated. We consider the N-fold degenerate Hubbard model defined on a lattice

W. D. Langer

A new solution for the narrow band Hubbard model is developed and the results for the one particle Green functions are presented. The spectral density has poles and resonance terms, and is exact for zero bandwidth. The antiferromagnetic state and transition temperature are studied.