1995 Fiscal Year Final Research Report Summary
Field Theoretical Methods in Condensed Matter Physics
| Project/Area Number |
06044043
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | Joint Research |
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| Research Institution | University of Tokyo |
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Principal Investigator |
KOHMOTO Mahito Institute for Solid State Physics, University of Tokyo Associate Professor, 物性研究所, 助教授 (40205349)
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| Co-Investigator(Kenkyū-buntansha) |
HATSUGAI Yasuhiro Department of Applied Physics, University of Tokyo, 工学部, 講師 (80218495)
WEN Xiao Gang Department of Physics, Massachusetts Institute of Technology, 物理学科, 助教授
ZEE Anthony Institute for Theoretical Physics & Department of Physics, University of Califor, 理論物理研究所, 教授
WU Yong-Shi Department of Physics, University of Utha, 物理学科, 教授
AVISHAI Yshai Department of Physics, Ben Gurion University, 物理学科, 教授
NAGAOSA Naoto Department of Applied Physics, University of Tokyo, 工学部, 助教授 (60164406)
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| Project Period (FY) |
1994 – 1995
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| Keywords | random two matrix model / exclusive statistice / Bethe ansatz / quantum group / fractal / fractional quantum Hall effect / randomness |
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| Research Abstract |
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.
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