Field Theoretical Methods in Condensed Matter Physics

凝聚态物理中的场论方法

• 批准号: 06044043
• 负责人: KOHMOTO Mahito
• 金额: $ 3.78万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for international Scientific Research
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06044043/
• 关键词: random two matrix model; exclusive statistice; Bethe ansatz; quantum group; fractal; fractional quantum Hall effect; randomness; 場の理論; 分数統計; 電子相関; ランダム行列; ユニバーサリティー

The purpose of this project is to develop theoretical studies of various phenomena in condensed matter physics by the field theoretical and numerical methods. The continuous discussions and collaborations with active researchers in the United States of America and Israel who are familiar in these techniques.1) To find a new universality class in disorder systems, the random two-matrix model was studied by Avishai, Hatsugai and Kohmoto. It was clarified that the level repulsion is stronger than the usual unitary-Gaussian ensemble by calculating correlations between two energies.2) Nagaosa and Kohmoto studies the effective field theory for the fractional quantum Hall effect. A quite natural way for having the gauge invariance is proposed without adding any additional terms to the action. The quantization of the Hall current is obtained. Discussions with Wen and Zee was helpful and stimulating in this work.3) A two dimensional model with random bond or random magnetic field is studied by Hatsugai, Wen and Kohmoto. It was shown that near zero energy, the system can be described by two copies of Dirac fermions with random imaginary chemical potential, random real mass and random imaginary gauge field. Using the discussion of Ludwig et.al., it is suggested that this model is critical st zero energy and weak randomness.

本项目的目的是通过场论和数值方法对凝聚态物理中的各种现象进行理论研究。1)为了寻找无序系统中新的普适类，Avishai，Hatsugai和Kohmoto研究了随机双矩阵模型。2)Nagaosa和Kohmoto研究了分数量子霍尔效应的有效场论。提出了一种非常自然的具有规范不变性的方法，而不需要在作用量上增加任何额外的项。得到了霍尔电流的量子化。3)Hatsugai，Win和Kohmoto研究了具有随机键或随机磁场的二维模型。结果表明，在能量接近于零的情况下，系统可以用具有随机虚化学势、随机实质量和随机虚规范场的两个Dirac费米子来描述。利用Ludwig等人的讨论，认为该模型具有临界零能量和弱随机性。

项目成果

T.S.Kobayakawa,Y.Hatsugai,M.Kohmoto,and A.Zee: ""Universal Correlations between Eigenvalues of Random Matrices"" Phys.Rev.E. 51. 5365 (1995)

T.S.Kobayakawa、Y.Hatsugai、M.Kohmoto 和 A.Zee：““随机矩阵特征值之间的通用相关性””Phys.Rev.E。

N.Nagaosa: "Non magnetic Impurity in Spin Gap State" Phys.Rev.B. (出版予定).

N.Nagaosa：“自旋间隙状态下的非磁性杂质”Phys.Rev.B（待出版）。

N.Nagaosa and M.Kohmoto: "Edge and Bulk of the Fractional Hall Liquids" Phys.Rev.Lett.(1995). to be published.

N.Nagaosa 和 M.Kohmoto：“分数霍尔液体的边缘和体积”Phys.Rev.Lett.(1995)。

N.Nagaosa: "Tunneling through a barrier in a Coulombgos confined in a quantum wire." J.Phys.Soc.Jpn.63(2). 413-415 (1994)

N.Nagaosa：“穿过量子线中限制的库仑戈势垒。”

Y.Avishai,Y.Hatsugai,and M.Kohmoto: ""Two-Matrix Models and Their Possible Relevance to Disorder Systems"" to be published in Phys.Rev.B.

Y.Avishai、Y.Hatsugai 和 M.Kohmoto：“双矩阵模型及其与无序系统的可能相关性”将在 Phys.Rev.B 上发表。