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arXiv:cond-mat/9402047

Critical Properties of the Mott Transition in the Hubbard Model

Goetz Moeller, Qimiao Si A, Gabriel Kotliar, Marcelo J. Rozenberg

Published Feb 10, 1994• 0 citations
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Abstract

We introduce a systematic low-energy approach to strongly correlated electron systems in infinite dimensions, and apply it to the problem of the correlation-induced metal-insulator transition in the half-filled Hubbard model. We determine the low-energy scaling functions of the metallic state, including the single-particle Green function and dynamical spin susceptibility, as well as thermodynamic properties and relate them to experimental data in transition metal oxides.

DOI
10.48550/arxiv.cond-mat/9402047

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We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.
The Mott-Hubbard transition in the half-filled Hubbard model is studied analytically on a Bethe lattice for the paramagnetic state and the classical N\'eel state. The single-particle density of states is obtained by calculating the one-particle Green's function represented by the Lanczos infinite continued fraction. The paramagnetic solution shows that the Mott-Hubbard transition is signaled by both collapsing Hubbard bands at Uc{\mathit{U}}_{\mathit{c}}Uc​=2t∗{\mathit{t}}_{\mathrm{*}}t∗​ and a sharp Lorentzian peak appearing at midgap at UUc{\mathit{U}}_{\mathit{c}}Uc​. For the N\'eel state, however, the system becomes an insulator for U>0. We also obtain the specific heat and entropy for both the metallic and insulating regimes. Our analytic work reproduces the key results obtained by numerical method in infinite dimensions.
Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.
A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported.