Wide applications of the renormalization group

重整化群的广泛应用

• 批准号: 14340077
• 负责人: SONODA Hidenori
• 金额: $ 9.34万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340077/
• 关键词: exact renormalization group; density matrix renormalization group; gauge theories; tensor product variational method; 繰り込み; カイラル対称性; 密度行列くりこみ群; f電子系; 磁気異方性; 繰り込み群; 完璧作用

We have applied renormalization group (RG) techniques to both quantum field theory and statistical physics. The research in quantum field theory was led by Sonoda, and that in statistical physics by Nishino.In the applications to quantum field theory, the following results have been obtained:1. Parametrization of the solutions to the exact RG equations was introduced by examining the behavior of the solutions at a large momentum cutoff2. The exact RG equation has been reformulated as an integral equation, which gives a formal perturbative solution.3. The parametrization described in 1 has been applied to QED. The Ward identities constrain the parameters.In the applications to statistical physics, the following results have been obtained:1. Avery fast numerical method of the product wave function RG has been developed.2. Generalizing the matrix products to tensor products, we have formulated the tensor product RG variational method, which can be considered as an extension of the density matrix RG method to higher dimensional systems.3. Extending the density matrix RG method, we have obtained the stochastic light-cone density matrix RG and the method of snapshot generation. These have been applied to statistical systems, resulting in phase diagrams of 2-and 3-dimensional ANNNI models, and the symmetric 16-vertex model.

我们已将重正化群 (RG) 技术应用于量子场论和统计物理学。园田主导了量子场论的研究，西野主导了统计物理学的研究。在量子场论的应用方面，取得了以下成果： 1．通过检查大动量截止下解的行为，引入了精确 RG 方程解的参数化2。精确的RG方程被重新表述为积分方程，给出了形式的微扰解。 3． 1 中描述的参数化已应用于 QED。 Ward恒等式对参数进行约束。在统计物理应用中，得到了以下结果： 1．发展了一种快速的乘积波函数RG数值方法。 2．将矩阵积推广到张量积，提出了张量积RG变分法，该方法可以看作是密度矩阵RG法向高维系统的推广。 3．对密度矩阵RG方法进行扩展，得到了随机光锥密度矩阵RG和快照生成方法。这些已应用于统计系统，产生 2 维和 3 维 ANNNI 模型以及对称 16 顶点模型的相图。

项目成果

E.Kaneshita, M.Ichioka, K.Machida: "Study of phonon anomalies in stripe phase of high Tc cuprates"Physical B. (To be published).

E.Kaneshita、M.Ichioka、K.Machida：“高 Tc 铜酸盐条纹相中声子异常的研究”物理 B.（待出版）。

Stable optimization of tensor product variational functions

张量积变分函数的稳定优化

• 发表时间: 2003
• 期刊: Prog. Theo. Phys. 110
• 作者: A.Gendiar;T.Nishino
• 通讯作者: T.Nishino

Bootstrapping perturbative perfect actions,

引导扰动的完美动作，

• 发表时间: 2003
• 期刊: Phys. Rev. D67
• 作者: E.Itou;K.Higashijima;H.Sonoda
• 通讯作者: H.Sonoda

Snapshot Observation for 2D Classical Lattice Models by CTMRG

CTMRG 的二维经典晶格模型快照观察

• 期刊: JPSJ supplement (accepted for publication)(未定)
• 作者: K.Ueda;R.Otani;Y.Nishino;A.Gendiar;T.Nishino
• 通讯作者: T.Nishino

A.Gendiar: "Stable Optimization of Tensor Product Variational Functions"Prog.Theor.Phys.. 110. 691-699 (2003)

A.Gendiar：“张量积变分函数的稳定优化”Prog.Theor.Phys.. 110. 691-699 (2003)