Field Theoretical Methods in Condensed Matter Physics

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.