Anyons as Elementary Field Quanta

S Bhattacharjee, Julian May-Mann, S. Raghu

We obtain integer and fractional quantum Hall crystals as ground states of a two-dimensional electron system subject to a strong perpendicular magnetic field and a periodic potential. For certain fractional states, we show that the Hall crystal can constitute an anyon crystal, with a periodic ordering of well-defined anyons. We find that the latter states can be stabilized at odd denominator Landau level filling fractions when Landau level mixing is sufficiently weak, and near half-filling of the underlying lattice. These phases are obtained from a mean-field analysis of an effective lattice model of bosons attached to an odd number of flux quanta, which transmutes their statistics to that of electrons. In boson coordinates, the Hall crystal is a supersolid: a superfluid with charge order. Under strong interactions, vortex-anti-vortex pairs spontaneously nucleate in the supersolid, realizing a crystalline state of anyons.

Alberto Lerda A, S. Sciuto

G. Baskaran, Erio Tosatti, L. YU

The RVB state is a singlet quantum liquid which can support periodic or fluid-like quantum circulation around the elementary plaquette in two dimensions. In the s + id phase there is a half flux quanta of circulation in every elementary plaquette. We show that the holons in the presence of this lattice of circulation have a two-valley structure, as opposed to "s"or "d" states, which have a single valley. Using an effective holon Hamiltonian, we study the mean-field properties of the two-valley holon condensate, and compare its energy with the single valley case. A transition from the "d" to the "s + id" state is predicted with increasing hole concentration for sufficiently large Hubbard U. Some speculations are offered about the general case of a fluid-like distribution of flux quanta.