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Physical review. B, Condensed matter

Path-integral theory of the metal-insulator transition in the three-dimensional Hubbard model

Norikazu Tomita, Masahiro Yamazaki, Keiichirō Nasu

Published Jul 30, 2003• 5 citations
Publisher

Abstract

We study, by using the quantum Monte Carlo simulation of path-integral form, how the gap is developed in the density of state (DOS) and optical conductivity of the three-dimensional half-filled Hubbard model as a function of the temperature. It is shown that the DOS has a coherent peak just on the Fermi level in the high-temperature region. However, it moves to the high-binding-energy side when the temperature is lowered. The DOS just on the Fermi level is decreased as the decrease of the temperature, and eventually, a gap opens in the DOS. The Drude component in the optical conductivity also decreases with temperature, but it can remain relatively large compared to the DOS at the Fermi level, if the DOS is finite there. We show that the experimentally observed photoemission and optical conductivity spectra of ${\mathrm{CaVO}}_{3}$ are explained within the present theoretical framework effectively and consistently.

DOI
10.1103/physrevb.68.035117

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We study, by using the quantum Monte Carlo simulation of path-integral form, how the gap is developed in the density of state (DOS) and optical conductivity of the three-dimensional half-filled Hubbard model as a function of the temperature. It is shown that the DOS has a coherent peak just on the Fermi level in the high-temperature region. However, it moves to the high-binding-energy side when the temperature is lowered. The DOS just on the Fermi level is decreased as the decrease of the temperature, and eventually, a gap opens in the DOS. The Drude component in the optical conductivity also decreases with temperature, but it can remain relatively large compared to the DOS at the Fermi level, if the DOS is finite there. We show that the experimentally observed photoemission and optical conductivity spectra of CaVO3{\mathrm{CaVO}}_{3}CaVO3​ are explained within the present theoretical framework effectively and consistently.
Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half-filling we observe a gradual crossover from a metal with a Drude peak at ω = 0 in the optical conductivity to an insulator as a function of U for temperatures above the antiferromagnetic phase transition. When doped, the "insulator" becomes a Fermi liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a T 2 -coefficient in the low-temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.
Dynamic properties of the three-dimensional single-band Hubbard model are studied using quantum Monte Carlo combined with the maximum entropy technique. At half-filling, there is a clear gap in the density of states and well-defined quasiparticle peaks at the top (bottom) of the lower (upper) Hubbard band. We find an antiferromagnetically induced weight above the naive Fermi momentum. Upon hole doping, the chemical potential \ensuremath{\mu} moves to the top of the lower band where a robust peak is observed. Results are compared with spin-density-wave mean-field and self-consistent Born approximation results, and also with the infinite-dimensional (D=\ensuremath{\infty}) Hubbard model, and experimental photoemission for three-dimensional transition-metal oxides. \textcopyright{} 1996 The American Physical Society.
We study electric transport near the Mott metal-insulator transition in a triangular-lattice Hubbard model at half filling. We calculate optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ based on a cellular dynamical mean-field theory including vertex corrections inside the cluster. Near the Mott critical end point, a Drude analysis in the metallic region suggests that the change in the Drude weight is important rather than that in the transport scattering rate for the Mott transition. In the insulating region, there emerges an ``in-gap'' peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ at low $\ensuremath{\omega}$ near the Mott transition, and this smoothly connects to the Drude peak in the metallic region with decreasing Coulomb repulsion. We find that the weight of these peaks exhibits a power-law behavior upon controlling Coulomb repulsion at the critical temperature. The obtained critical exponent suggests that conductivity does not correspond to magnetization or energy density of the Ising universality class in contrast to several previous works.
We study the transition from paramagnetic metal to paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model at half-filling. Working at the moderately high temperature T=0.33*t where the spin correlation length has dropped to 1.5 lattice spacings, and scanning the interaction strength U, we observe an unambiguous metal-insulator transition with onset at U_c=4t. In the metallic phase there are no indications of any `correlation narrowing' of the band width, nor for any decrease of spectral weight at the Fermi energy. The Mott-Hubbard gap opens gradually with increasing U and is accompanied by the formation of side bands near the Fermi energy. In the first stages of gap formation the gap opens at (pi,0), reminiscent of the `pseudogap' phenomenology in cuprate superconductors.
The optical conductivity, \ensuremath{\sigma}(\ensuremath{\omega}), of the two-dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane dc resistivity, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$, is also evalauted. We find that at large U/t and temperature T, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$ is approximately linear with temperature. We also observed that \ensuremath{\sigma}(\ensuremath{\omega}) displays charge excitations, a midinfrared (MIR) band, and a Drude peak. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than 1/${\mathrm{\ensuremath{\omega}}}^{2}$ at energies smaller than the insulator gap near half filling.