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Physical Review Letters

Metal-insulator transition in a generalized Hubbard model

Kristel F. L. Michielsen, Hans A. De Raedt, T. Schneider

Published Mar 2, 1992• 20 citations
Publisher

Abstract

An extension of the Hubbard model, introduced by Montorsi and Rasetti, is studied using exact diagonalization and quantum Monte Carlo methods. Our numerical results for the static and dynamic properties of one- and two-dimensional systems strongly suggest the occurrence of a metal-insulator transition.
DOI
10.1103/physrevlett.68.1410

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An overview of lattice models for strongly correlated electrons is given. A detailed study is presented of a model recently introduced by Montorsi and Rasetti. Analytical, exact diagonalization and Quantum Monte Carlo techniques are employed to investigate the static and dynamic properties of this model. The complete ground state phase diagram of the one-, two- and three-dimensional model is given. The Montorsi-Rasetti model is shown to exhibit a metal-insulator transition of the Mott type, independent of the dimensionality of the lattice, and has a ferromagnetic phase. Results for the two-dimensional Montorsi-Rasetti model strongly suggest the occurrence of a phase transition at finite temperatures.
A generalized Hubbard model with correlated hoppings is studied at half filling using exact diagonalization methods. For certain values of the hopping parameters our results for several static properties, the Drude weight and the single-particle spectra function, suggest the occurrence of a metal-insulator transition (MIT) at a finite value of the local Coulomb interaction Uc{\mathit{U}}_{\mathit{c}}Uc​. We identify the regions of the hopping parameters where the MIT is of the Mott type. In these regions, for large UUc{\mathit{U}}_{\mathit{c}}Uc​, we find a ferromagnetic ground state.
We use quantum Monte Carlo methods to determine T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 Green functions, $G(\stackrel{\ensuremath{\rightarrow}}{r},\ensuremath{\omega})$, on lattices up to $16\ifmmode\times\else\texttimes\fi{}16$ for the 2D Hubbard model at U/t=4U/t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4U/t=4. For chemical potentials $\ensuremath{\mu}$ within the Hubbard gap $|\ensuremath{\mu}|<{\ensuremath{\mu}}_{c}$ and at long distances $\stackrel{\ensuremath{\rightarrow}}{r}$, $G(\stackrel{\ensuremath{\rightarrow}}{r},\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\mu})\ensuremath{\sim}{e}^{\ensuremath{-}|\stackrel{\ensuremath{\rightarrow}}{r}|/{\ensuremath{\xi}}_{l}}$ with critical behavior ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.26\ifmmode\pm\else\textpm\fi{}0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/4$ and dynamical exponent z=4z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4z=4. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ and z=2z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2z=2.
Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.