Field Theoretical Methods in Condensed Matter Physics

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。与美国和以色列熟悉这些技术的活跃研究人员的持续讨论和合作。1）为了在无序系统中找到一个新的普适类，Avishai，Hatsugai和Kohmoto研究了随机双矩阵模型。通过计算两个能量之间的关联，阐明了能级排斥比通常的么正高斯系综更强。2）Nagaosa和Kohmoto研究了分数量子霍尔效应的有效场理论。提出了一种在不增加作用量任何附加项的情况下具有规范不变性的很自然的方法。得到了霍尔电流的量子化。3）Hatsugai，Wen和Kohmoto研究了具有随机键或随机磁场的二维模型。结果表明，在能量接近于零时，系统可以用两个具有随机虚化学势、随机真实的质量和随机虚规范场的狄拉克费米子来描述。利用路德维希等人的讨论，结果表明，该模型是零能弱随机的临界模型。

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.