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Physical Review Letters

Mott transition in thed=∞ Hubbard model at zero temperature

X. Y. Zhang, Marcelo J. Rozenberg, Gabriel Kotliar

Published Mar 15, 1993• 343 citations
Publisher

Abstract

Using a combination of perturbation theory and quantum Monte Carlo, we elucidate the behavior of the single-particle Green's function and the local spin-spin correlation function near the Mott transition in the infinite dimensional Hubbard model at half filling. The model has three fixed points: the Fermi liquid phase qualitatively described by the Brinkman-Rice picture, the insulating phase resembling Hubbard's solution, and an unstable Mott point which connects the two.

DOI
10.1103/physrevlett.70.1666

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Using a combination of perturbation theory and quantum Monte Carlo, we elucidate the behavior of the single-particle Green's function and the local spin-spin correlation function near the Mott transition in the infinite dimensional Hubbard model at half filling. The model has three fixed points: the Fermi liquid phase qualitatively described by the Brinkman-Rice picture, the insulating phase resembling Hubbard's solution, and an unstable Mott point which connects the two.
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We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.
We investigate the metal-insulator transition of the one-dimensional SU(N)\mathrm{SU}(N)SU(N) Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half filling ${(k}_{F}=\ensuremath{\pi}{/Na}_{0})$ is conjectured for N>2.N>2.N>2. Expressions for the charge and spin velocities as well as for the Luttinger-liquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger-liquid parameters as a function of the Coulomb interaction UUU are given for the cases N=3N=3N=3 and N=4.N=4.N=4. Our results strongly support the existence of a Mott-Hubbard transition at a nonzero value of the Coulomb interaction. We find ${U}_{c}\ensuremath{\sim}2.2$ for N=3N=3N=3 and ${U}_{c}\ensuremath{\sim}2.8$ for N=4.N=4.N=4.