INTEGER QUANTUM HALL-EFFECT FOR HARD-CORE BOSONS AND A FAILURE OF BOSONIC CHERN-SIMONS MEAN-FIELD THEORIES FOR ELECTRONS AT A HALF-FILLED LANDAU-LEVEL

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These eff ective theories are usually studied by perturbing around a mean-field approximation, so the question as to whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson sys tem in a uniform external field such that there is one flux quantum pe r particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at h alf-filling to a boson system at integer filling fails.