Theorles of Superconductivity and Quantum Hall Effect Via Chem-Simons Gauge Theory.

通过化学-西蒙斯规范理论的超导理论和量子霍尔效应。

• 批准号: 03640256
• 负责人: ISHIKAWA Kenzo
• 金额: $ 0.83万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640256/
• 关键词: Strong correlation; Quantum Hall effect; Fractional Hall effect; One dimensional system; Vortex; Correlation function; Bi-local mean field; トポロジー; チャーン・サイモンゲージ理論; bi-local場; 強相関電子系; ラッティンジャー流体; K-T転移; 強磁場; 2次元電子系; 量子ホ-ル効果; Laughlin関数; 分子場

Bi-local mean field theory has been applied to strongly correlated electron systems. Especially last year, the vortex solutions of quantum Hall system which are non-linear and topological excitations have been analyzed, and the same method was applied to one dimensional 1/7^2 interacting systems. Main results are the following :(i) Charged vortex solutions and neutral vortex solutions of quantum Hall system are obtained.(ii) Bi-local mean field theory gives a reasonable value to the ground state energy in one dimensional system.(iii) Exponents of correlation functions satisfy the Luttinger liquid relation but are in dis-agreement with those of conformal field theory.

双局域平均场理论已应用于强相关电子系统。特别是去年，我们对非线性拓扑激发的量子霍尔系统的涡旋解进行了分析，并将同样的方法应用于一维1/7^2相互作用系统。主要结果如下：(i)得到了量子霍尔系统的带电涡旋解和中性涡旋解。(ii)双局域平均场理论给出了一维系统中基态能量的合理值。(iii)指数相关函数满足 Luttinger 液体关系，但与共形场论的关系不一致。

项目成果

K.Ishikawa: "A mean Field Theory for the Quantum Hall Liquid II, -Vortex-" Prog.Theo.Phys.vol.91. 237-249 (1994)

K.Ishikawa：“量子霍尔液体 II 的平均场论，-涡旋-”Prog.Theo.Phys.vol.91。

K.Ishikawa: "Field Theory in a Strong magnetic Field and the Quantum Hall Effect" Progress of Theoretical Physics. Supp.107. 167-183 (1992)

K.Ishikawa：“强磁场中的场论和量子霍尔效应”理论物理进展。

K.Ishikawa: "A Mean Field Theory for the Quantum Hall Liquid II.-Vortex-" Prog.Theor.Phys.91. 237-249 (1994)

K.Ishikawa：“量子霍尔液体的平均场理论 II.-涡旋-”Prog.Theor.Phys.91。

N.Imai: "Quantum Theory of a Relativistic Particle with Torsion and Chern-Simons Gauge Theory" Prog.Theor.Phys.88. 351-376 (1992)

N.Imai：“具有挠场的相对论粒子的量子理论和陈-西蒙斯规范理论”Prog.Theor.Phys.88。

N.Imai: "Quantum Theory of a relativistic particle with Torsion and Cherm-Simons G.Thesy." Prog.Theor.Phys.88. 351-376 (1992)

N.Imai：“相对论粒子的量子理论与挠场和 Cherm-Simons G.Thesy。”