Do Hard-core Bosons Exhibit Quantum Hall Effect?

We motivate the study of hard-core bosons in an external magnetic eld by describing anyons either as fermions or hard-core bosons with gauge-ux attached to them. We brieey review earlier attempts to address this problem. We show why quantum Hall eeect (QHE) for hard-core bosons can occur in the thermodynamic limit and use a variational trial wavefunction approach to identify the lling factors where QHE may be seen. The question of whether or not a gas of anyons 1 forms a superruid at certain statistics parameters still remains an interesting and unresolved theoretical problem. Techniques developed for fermions and bosons cannot be applied to study this problem because the essentiaìanyon' nature of the particles prevents even non-interacting many anyon states from being written as simple products of single anyon states. Thus, the many anyon problem has to be tackled as an intrinsically interacting problem even when the anyons are free. The (by now) standard route to the study of anyons involves their representation as conventional particles (fermions or bosons) with gauge ux attached to them. The amount of ux determines the statistics-i:e:, e iq=2 e ii (1) where q and are the charge and ux of the two charge-ux composites representing the anyons and is the statistics parameter. Moreover, the conventional particles have to be chosen to be hard-core, (automatically satissed by fermions, but needs to be imposed on bosons) because the underlying anyons are hard-core. This interacting problem can now be studied using various approximation techniques such as series(cluster) expansions 2 at low temperatures and high densities, mean eld (MF) theories 3 at high temperatures and low densities and even exact solutions 4 for a small number of particles.