Renormalization-Group Approach to the Quantum Hall Effect by Misha Raikh INSCC 110, 3:30pm Monday, November 30, 1998 Abstract The discovery of the quantum Hall effect by von Klitzing et.al. [K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. {\bf 42}, 673 (1980)] in 1980 is one of the most fascinating discoveries in condensed matter physics. This discovery was praised with the Nobel Prize in 1985. One of the manifestations of the quantum Hall effect is that at low temperatures a system of two-dimensional electrons undergoes an insulator-metal-insulator transition as external perpendicular magnetic field changes within a narrow interval around some discrete value. This interval shrinks as the temperature decreases. Theoretical studies of electronic states of two-dimensional electrons in a perpendicular magnetic field are traditionally carried out with the use of numerical simulations. Most of simulations employ the network model [J. T. Chalker and P. D. Coddington, J. Phys. C {\bf 21}, 2665 (1988).] which reduces the solution of the Schroedinger equation to the quantum percolation problem. In our work we generalize the real-space renormalization group procedure for the classical percolation to the case of the quantum percolation and derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find the numerical solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations. Request for preprints and reprints send to the speaker at