Geometric Disorder in the Integer Quantum Hall Transition
Guest Speaker, Noah Charles will discuss the role of geometric disorder in the integer quantum hall transition.
Quantum phase transitions are characterized by universal critical properties that are sensitive only to the symmetries of the system in question. In a physical sample, disorder will break all but a few of these symmetries; the inclusion of different types of disorder in the model therefore affects its universality class.
A recent paper (Gruzberg et al. 17) argued that a certain kind of geometric disorder in models for the integer quantum Hall transition may change the universal critical properties of the transition and that a continuum model in the same universality class should be coupled to a stochastic background curvature. We, therefore, examine a Dirac Hamiltonian on a curved Riemann surface that has been demonstrated (Ludwig et al. 94) to display an Integer Quantum Hall transition on a flat plane. We conclude that this model lies in an Integer Quantum Hall universality class by determining the anomalous multifractal exponents.