A Vortex Lattice of Anyons in Strongly Correlated Systems

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.

G. Rosenberg, Babak Seradjeh, Conan Weeks +1 more

弘之 森

A. P. Protogenov

The present state of the gauge theory of high-temperature superconductivity in strongly-correlated two-dimensional spin systems is reviewed. Basic ideas on the statistics of elementary excitations in spatially two-dimensional systems are presented and are used in an analysis of the structure of the energy spectrum and the form of the wave function of a set of anyon quasiparticles in both the long-wave continuous and lattice limits. The continuous and lattice theories are used to classify the phase states, and the hierarchy of phase transitions is described in terms of the topological quantum field theory. Thermodynamic and electrodynamic properties of anyon systems are described, and the experimental consequences of the Chern–Simons theory of high-Tc superconductivity are discussed.

Michael L. Wall

Uwe R. Fischer, Peter O. Fedichev, Alessio Recati

We discuss the feasibility of quantum Hall states of vortices in trapped low-density two-dimensional Bose gases with large particle interactions. For interaction strengths larger than a critical dimensionless 2D coupling constant g c ≈ 0.6, upon increasing the rotation frequency, the system is shown to spatially separate into vortex lattice and melted vortex lattice (vortex liquid) phases. At a first critical frequency, the lattice melts completely, and strongly correlated vortex and particle quantum Hall liquids coexist in inner and outer regions of the gas cloud, respectively. Finally, at a second critical frequency, the vortex liquid disappears and the strongly correlated particle quantum Hall state fills the whole sample.