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Physical review. B, Condensed matter

Transition characteristics of a Mott-Hubbard system in large dimensions

Jongbae Hong, Tae‐Suk Kim

Published Nov 15, 2000• 1 citation
Publisher

Abstract

We study the nature of metal-insulator transition in the paramagnetic state for the Hubbard model on the Bethe lattice. The single-particle density of states is calculated via the operator Lanczos method. Our study shows that the metal-insulator transition is continuous and there is no preformed gap. The quasiparticle weight vanishes linearly with the distance from the transition point ${(U}_{c})$ in agreement with results of iterative perturbation theory and exact diagonalization method. Our ${U}_{c}$ is comparable to that by the random dispersion approximation. Our result indicates non-Fermi-liquid feature at the transition point.

DOI
10.1103/physrevb.62.12581

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We study the nature of metal-insulator transition in the paramagnetic state for the Hubbard model on the Bethe lattice. The single-particle density of states is calculated via the operator Lanczos method. Our study shows that the metal-insulator transition is continuous and there is no preformed gap. The quasiparticle weight vanishes linearly with the distance from the transition point (Uc){(U}_{c})(Uc​) in agreement with results of iterative perturbation theory and exact diagonalization method. Our Uc{U}_{c}Uc​ is comparable to that by the random dispersion approximation. Our result indicates non-Fermi-liquid feature at the transition point.
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The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by quantum Monte Carlo simulations down to temperature T=W/140T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W/140T=W/140 ( W=bandwidthW\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{bandwidth}W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below ${T}_{\mathrm{IPT}}\ensuremath{\simeq}0.022W$, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325TIPT{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.325T}_{\mathrm{IPT}}T=0.325TIPT​. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.
A new nonperturbative method calculating the one-particle Green's function is introduced and applied to the Hubbard model. We show the metal–insulator transition in the paramagnetic ground state of the half-filled Hubbard model on a Bethe lattice with infinite connectivity. This method describes the transition regime appropriately. The analytic result using the continued fraction formalism which has a close relationship with present formalism is provided for comparison. As for the Hubbard model with doping, we obtain the optical conductivities and show the interesting features, such as midinfrared band and isobestic point. We also show that the sharp frequency-dependent behavior at large doping is the dispersed Drude type in this model.
The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands.
An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.
An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.