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Chinese Physics Letters

Numerical Study of Luttinger Liquid Regime of Two-Leg Hubbard Ladders

程宽, Yu-Liang Liu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

我们由 thedensity 矩阵重正常化组方法在 Luttinger 液体政体调查二腿的哈伯德梯子。在这个区域的契约概念的适用性在在梯子和链之间的幂定律腐烂代表，精力部件和 anti-bondoccupations 的量的比较被讨论。在有限哈伯德排斥 U 导致的债券和反契约乐队之间的相互作用被我们的数字结果强调。我们的量的结果为各种各样的分析途径的有效性的理由是有用的。

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我们由 thedensity 矩阵重正常化组方法在 Luttinger 液体政体调查二腿的哈伯德梯子。在这个区域的契约概念的适用性在在梯子和链之间的幂定律腐烂代表，精力部件和 anti-bondoccupations 的量的比较被讨论。在有限哈伯德排斥 U 导致的债券和反契约乐队之间的相互作用被我们的数字结果强调。我们的量的结果为各种各样的分析途径的有效性的理由是有用的。
We investigate two-leg Hubbard ladders in the Luttinger liquid regime by the density-matrix renormalization group method. Applicability of the bond concept in this region is discussed in a quantitative comparison of power-law decay exponents, energy components and anti-bond occupations between ladders and chains. The interaction between bond and anti-bond bands induced by finite Hubbard repulsion U is emphasized by our numerical results. Our quantitative results are useful for the justification of the validity of various analytical approaches.
We study the Luttinger-liquid parameter KρK_ρKρ​ of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent KρK_ρKρ​ is related to the charge susceptibility χcχ_cχc​ and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain KρK_ρKρ​ at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the numerical diagonalization for the Hubbard ladder. It shows that the perturbation calculation of KρK_ρKρ​ is reliable in the weak coupling regime.
Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in a magnetic field. Based on different magnetization behaviors, we found a disordered spin liquid, the Luttinger liquid, spin-polarized phases, and a classical regime. Our calculations in the Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on Cu2(C5H12N2)2Cl4 are due to a quasi-one-dimensional effect rather than three-dimensional ordering.