Development of New Numerical Renormalization Group Method and Its Application to Low-Dimensional Phase Transitions

新数值重正化群方法的发展及其在低维相变中的应用

• 批准号: 09640462
• 负责人: AKUTSU Yasuhiro
• 金额: $ 2.37万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640462/
• 关键词: numerical renormalization; DMRG; PWFRG; quantum spin; vicinal surface; magnetization process; roughening; higher dimension; 計算物理; 繰り込み群; 密度行列; 転送行列; 臨界現象; 強相関系

1. (1) For systems with asymmetric transfer matrices, we introduce the "renormalized identity" which allows us to constructed a numerical renormalization scheme where only the symmetric density matrices are involved. (2) We establish a universal asymptotic relation between the density matrix eigenvalue and the number of retained bases. (3) For 3D classical statistical system, we find an explicit construction scheme of local tensor which is an essential building block of the maximum-eigenvalue-state wavefunction of the transfer matrix, establishing a higher-dimensional extension of DMRG. We also show that 2D quantum system can be treated by an anisotropic limit of a 3D classical system.2. (1) We confirm the anomalous temperature dependence of the step tension in the surface model of NaCl-type crystal. (2) We calculate the anisotropic step tension and the crystal facet shape, from which we verified the validity of the renrmalized free random-walk picture for the step on a surface. (3) We … More study the vicinal surface with adsorption. We find that the attractive inter-step interaction emerges due to the adsorbate density fluctuation, and that there occurs a first-order phase transition due to the inter-step attraction.3. (1) From the accurate calculation of the M-H curve of the quantum spin chains, we show the validity of the δ-function bose-gas picture near the critical fields. (2) We discover the middle-field cusp singularity in the M-H curve for the S=1/2 spin ladder and S=1 bilinear-biquadratic chain. (3) For the honeycom latttice VBS-type AF spin model, we calculated correlation length and the sublattice magnetization. The S=3/2 bilinear-biquadratic AF spin model, we perform PWFRG-assisted variational calculation based on the product-of-tensors ansatz for the ground-state wavefunction. We find the first-order transition between the Neel and the disordered states. (4) We calculate transverse susceptibility for the 2D Ising-like models, to show that its temperature derivative has the same critical singularity as the specific heat.4. (1) We establish a method to calculate the free energy and the entropy by the PWFRG/DMRG, and apply it to obtain the zero-point entropy for fully-frustrated antiferromagnets. (2) We study the critical behavior of the 2D Ising-like system with linear defect, to find that the non-universal behavior of the critical exponents persists even if the 4-spin interactions are present. Also, the scaling relations between the defect exponents are confirmed. Less

1. (1)对于具有非对称传输矩阵的系统，我们引入了“重整化恒等式”，它允许我们构造一个只涉及对称密度矩阵的数值重整化方案。(2)我们建立了密度矩阵特征值与保留基数目之间的普适渐近关系。(3)对于3D经典统计系统，我们找到了局部张量的显式构造方案，该局部张量是传递矩阵的最大本征值状态波函数的重要组成部分，建立了DMRG的高维扩展。我们还证明了二维量子系统可以用三维经典系统的各向异性极限来处理. (1)我们证实了NaCl型晶体表面模型中阶跃张力的反常温度依赖性。(2)计算了各向异性台阶张力和晶体小面形状，验证了表面台阶的重整化自由随机行走图象的正确性。(3)我们 ...更多信息 用吸附法研究邻位表面。我们发现，吸附质密度的涨落导致了步间吸引作用的出现，并且由于步间吸引作用，发生了一级相变. (1)通过对量子自旋链的M-H曲线的精确计算，证明了临界场附近δ函数玻色气体图象的正确性。(2)我们发现了S=1/2自旋梯和S=1双线性双二次链的M-H曲线的中场尖点奇异性。(3)对于蜂窝晶格VBS-AF自旋模型，我们计算了关联长度和亚晶格磁化强度。在S=3/2的双线性双二次AF自旋模型中，我们对基态波函数进行了基于张量乘积的PWFRG辅助变分计算。我们发现了Neel态和无序态之间的一级跃迁。(4)计算了二维Ising类模型的横向磁化率，证明了其温度导数与比热具有相同的临界奇异性. (1)建立了一种利用PWFRG/DMRG计算自由能和熵的方法，并将其应用于全阻挫反铁磁体的零点熵计算。(2)我们研究了具有线性缺陷的二维Ising类系统的临界行为，发现即使存在4-自旋相互作用，临界指数的非普适行为仍然存在。此外，缺陷指数之间的标度关系被确认。少

项目成果

R.Sato: "Universal properties in the free energy of the asymmetric N-state vertex model"J. Phys. A. 32. 5599-5609 (1999)

R.Sato：“非对称 N 态顶点模型自由能的普遍性质”J.

R. Sato: "Universal properties in the free energy of the asymmetric N-state vertex model"J. Phys. A, Math. Gen.. 32巻. 5599-5609 (1999)

R. Sato：“非对称 N 态顶点模型的自由能的普遍性质”J. Phys A，数学 Gen.. 32. 5599-5609 (1999)

N. Akutru: "Statistical mechanical calculation of anisotropic step stiffness of a two-dimensional hexagonal lattice-gas model with next-nearest-neighbour interactions : application to Si(111) surface"J. Phys. Condens. Matter. 11巻. 6635-6652 (1999)

N. Akutru：“具有次近邻相互作用的二维六方晶格气体模型的各向异性阶跃刚度的统计力学计算：在 Si(111) 表面上的应用”J. Matter。 6635 -6652 (1999)

N.Akutsu: "Thermal evolution of step stiffness on Si (001) surface : Temperature-rescaled Ising -model approach" Phys.Rev.B. 57・8. R4233-R4236 (1998)

N.Akutsu：“Si (001) 表面阶梯刚度的热演化：温度重新调整的 Ising 模型方法”Phys.Rev.B. (1998)

N. Akutru: "Thermal Evolution of Step Stiffness on Si(001) Surface : Temperature-Rescaled Ising-Model Approach"Phys. Rev. B. 57巻. R4233-R4236 (1998)

N. Akutru：“Si(001) 表面阶梯刚度的热演化：温度重新调整的伊辛模型方法”Phys Rev. B. Vol. 57. R4233-R4236 (1998)