Quantum Phase Transition in d = ∞ Hubbard Model

Shinichi Saito, Hiroyuki Yoshimoto, Susumu Kurihara, Yasuo Suzuki

Published Sep 20, 1999• 0 citations

Abstract

我々は、無限大次元のHubbard模型をGutzwiller波動関数に反強磁性相関を取り入れることで以下のことを示した。Brinkman-Rice理論で記述されるFermi液体から反強磁性体ヘモット転移する際、有効質量は増大するが発散しない。ハーフ・フィリングでは、ハバード・ギャップが開くことで絶縁体化する。キャリアをドープすると反強磁性金属相が現れるが、ランダウのフェルミ液体論を反強磁性領域に拡張して解析した結果、この領域では準粒子間に引力が働く。従って、超伝導相を含む豊富な相が実現し、相互作用の大きさや粒子数を変化させることで量子相転移することが判明した。

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Abstract

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The

{\mathit{U}}_{\mathit{d}}

=\ensuremath{\infty} three-band Hubbard model on a two-dimensional

{\mathrm{CuO}}_{2}

network is studied based on a Gutzwiller wave function by use of the variational Monte Carlo (VMC) method, where

{\mathit{U}}_{\mathit{d}}

is the Coulomb repulsion between holes on the Cu site (hole picture). The VMC results are compared with those of the Rice-Ueda-type Gutzwiller approximation (GA) in a half-filled band, where the average number of holes per Cu site is n=1. In the GA the Brinkman-Rice (BR) transition occurs at a finite value of ${\mathrm{\ensuremath{\Delta}}}_{0}$=(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{d}}$)/2, and then the number of d holes becomes

{\mathit{n}}_{\mathit{d}}

=n=1. Whether the BR transition really occurs or not within the Gutzwiller wave function is discussed in detail. In finite systems the absence of the BR transition is shown analytically. The thermodynamic limit is examined assuming the asymptotic behavior of

{\mathit{n}}_{\mathit{d}}

is given by a scaling function. The results of the finite-size scaling analysis suggest the absence of the BR transition as that in the single-band Hubbard model.