Oral: Renormalization Group Studies of Interacting Electrons in a Magnetic Field

A long-standing challenge in condensed matter physics is to determine the effective interaction of non-relativistic electrons confined to a Landau level when the ratio of Coulomb to kinetic energy, \kappa, is not small. In this work, we present a Wilsonian renormalization group approach to tackle this problem. Our renormalization group program begins by projecting the Coulomb interaction onto a truncated Hilbert space containing N Landau levels. We then systematically integrate out each Landau level, sequentially reducing

N to N-1 and deriving the effective interactions. We found that when \kappa is large, such as 2 or 3, traditional second-order perturbation theory incorrectly predicts an attractive interaction in the m=0 Haldane pseudopotential, while our approach yields a physically accurate result. We further discuss extensions of our method to more complex two-dimensional electron gas systems, including AlAs and graphene.