Anderson transition in interacting electron systems

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The main objective of this research is to investigate the disorder induced metal-insulator transition in interacting electron systems. This problem is really difficult but there still are hints. In 2D electron systems in high magnetic fields, the interacting electron systems can be mapped to the systems with randomly varying magnetic fluxes. We have simulated this random flux systems numerically. We are planning to investigate the case where the fluctuations of fluxes are not only spatially but also temporally in the future project. Another possible approach is the scaling theory. For that purpose, we have analyzed in detail the Anderson transition in non-interacting systems, especially the boundary condition effect and the conductance distribution.The two dimensional Anderson transition is of interest even in the absence of interaction. That in the presence of spin-orbit interactions is especially interesting. We have determined the critical exponent of this system precisely, and investigated the effect of dephasing.We have also investigated the classical Coulomb gap using the genetic algorithm. The quantum Coulomb glass has also been investigated using the method of level statistics.