A Typology for Quantum Hall Liquids

Abstract

There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the Types of superconductor are distinguished by this response, so too for QHLs: a typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between Type I and Type II behavior, the CSLG action has a "Bogomol'nyi point," where the quasi-holes (vortices) are non-interacting - at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wavefunctions. All Types of QHLs are capable of giving rise to quantized Hall plateaux.