Critical Exponents for the Quantum Hall and Quantum Spin Hall Effect
Speaker: Tomi Ohtsuki, Sophia University, Japan
Department: Electrical Engineering
Location: Engineering Quadrangle B205
Date/Time: Tuesday, October 9, 2012, 4:00 p.m. - 5:00 p.m.
The plateau transitions of the quantum Hall effect is one of the most extensively studied quantum critical phenomena in condensed matter physics. It is described by the exponent \nu, which describes the divergence of the localization length. Experimentally, the exponent is related to the slope of the Hall conductivity between the plateaus.
Since the discovery of the quantum Hall effect, the critical exponent has been studied extensively, but the precise value remains elusive. One of the difficulties is the occurrence of corrections to scaling, which change only very gradually with the system size. These slowly changing corrections make it numerically very demanding to estimate the behavior in the thermodynamic limit. A few years ago, we succeeded in estimating the value to be 2.59, which is significantly larger than the previously widely accepted value of 2.37. We discuss the implication of this new value for experiment and the conformal field theory. We also report the estimate of \nu for quantum spin Hall effect, which seems to be consistent with the values for the standard symplectic universality class.