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理论物理通讯：英文版

Fermion Coherent State Studies of One-Dimensional Hubbard Model

Lin Lin, Ji, Gao Gao, Xianlong, Wang, Ke-Lin

Published Jan 1, 2007• 0 citations
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Abstract

我们在场 one-dimensionalHubbard 模型的扎根的状态的比较研究。我们首先使用在由介绍一个洞操作员并且考虑二的相互作用的费密液体理论的框架的协调州的方法配对的新费米子电子一豺犬。我们作为|> =构造哈伯德模型的扎根的状态[ f + ∑′φc _( k_1 σ_ 1 )h_( k_2 σ_ 2 )c_( k_3 σ_ 3 )h_( k_4 σ_ 4 ) ∏e xp ( ρc _( k_1 σ_ 1 )h_( k_2 σ_ 2 ))]φ 和ρ 是联合常数的| >_0 。我们的结果当时与变化方法的那些相比，密度功能的理论基于准确可解决的 Bethe ansatz 解决方案，象到无限的系统的准确结果一样的变化 Monto-Carlo 方法(VMC ) 。我们发现在费米子之间的令人满意的同意协调州的计划和 VMC 数据，并且提供一幅新图画处理强烈相关的系统。

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We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ∣⟩ = [ f +∑'φ c † k 1 σ 1 h † k 2 σ 2 c † k 3 σ 3 h † k 4 σ 4 ∏exp(ρ c † k 1 σ 1 h † k 2 σ 2 )]∣⟩ 0 , where φ and ρ are the coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto–Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.

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Following a recent group theoretical quantization of the symplectic space S={(phi in R mod 2pi, p>0)} in terms of irreducible unitary representations of the group SO(1,2) the present paper proposes an application of those results to the old problem of quantizing modulus and phase in interference phenomena: The self-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond to the classical observables p cos(phi), -p sin(phi) and p > 0 the Poisson brackets of which obey that Lie algebra, too. For the irreducible unitary representations of the positive series the modulus operator K_3 has the positive discrete spectrum {n+k, n=0,1,2,...; k > 0}. Self-adjoint operators for cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2 and - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired properties for k >0.32. Some matrix elements with respect to number eigenstates and with respect to coherent states are calculated. One conclusion is that group theoretical quantization may be tested by quantum optical experiments.

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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。

•Sep 20, 1999•0 citations
我们在场 one-dimensionalHubbard 模型的扎根的状态的比较研究。我们首先使用在由介绍一个洞操作员并且考虑二的相互作用的费密液体理论的框架的协调州的方法配对的新费米子电子一豺犬。我们作为|> =构造哈伯德模型的扎根的状态[ f + ∑′φc ( k_1 σ 1 )h_( k_2 σ_ 2 )c_( k_3 σ_ 3 )h_( k_4 σ_ 4 ) ∏e xp ( ρc ( k_1 σ 1 )h_( k_2 σ_ 2 ))]φ 和ρ 是联合常数的| >_0 。我们的结果当时与变化方法的那些相比，密度功能的理论基于准确可解决的 Bethe ansatz 解决方案，象到无限的系统的准确结果一样的变化 Monto-Carlo 方法(VMC ) 。我们发现在费米子之间的令人满意的同意协调州的计划和 VMC 数据，并且提供一幅新图画处理强烈相关的系统。
We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ∣⟩ = [ f +∑'φ c † k 1 σ 1 h † k 2 σ 2 c † k 3 σ 3 h † k 4 σ 4 ∏exp(ρ c † k 1 σ 1 h † k 2 σ 2 )]∣⟩ 0 , where φ and ρ are the coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto–Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.
Following a recent group theoretical quantization of the symplectic space S={(phi in R mod 2pi, p>0)} in terms of irreducible unitary representations of the group SO(1,2) the present paper proposes an application of those results to the old problem of quantizing modulus and phase in interference phenomena: The self-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond to the classical observables p cos(phi), -p sin(phi) and p > 0 the Poisson brackets of which obey that Lie algebra, too. For the irreducible unitary representations of the positive series the modulus operator K_3 has the positive discrete spectrum {n+k, n=0,1,2,...; k > 0}. Self-adjoint operators for cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2 and - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired properties for k >0.32. Some matrix elements with respect to number eigenstates and with respect to coherent states are calculated. One conclusion is that group theoretical quantization may be tested by quantum optical experiments.
A typical classical interference pattern of two waves with intensities I_1, I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3 observables p = sqrt{I_1 I_2}, p cosϕand -p sinϕ. They are, e.g. the starting point for the semi-classical operational approach by Noh, Fougeres and Mandel (NFM) to the old and notorious phase problem in quantum optics. Following a recent group theoretical quantization of the symplectic space S = {(phi in R mod 2pi, p > 0)} in terms of irreducible unitary representations of the group SO(1,2) the present paper applies those results to that controversial problem of quantizing moduli and phases of complex numbers: The Poisson brackets of the classical observables p cosϕ, -p sinϕand p > 0 form the Lie algebra of the group SO(1,2). The corresponding self-adjoint generators K_1, K_2 and K_3 of that group may be obtained from its irreducible unitary representations. For the positive discrete series the modulus operator K_3 has the spectrum {k+n, n = 0, 1,2,...; k > 0}. Self-adjoint operators for cos phi and sin phi can be defined as ((1/K_3)K_1 + K_1/K_3)/2 and -((1/K_3)K_2 + K_2/K_3)/2 which have the theoretically desired properties for k > or = 0.5. The approach advocated here solves, e.g. the modulus-phase quantization problem for the harmonic oscillator and appears to provide a full quantum theoretical basis for the NFM-formalism.
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。