Composite anyons on a torus

Abstract

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Finally, we obtain from these wave functions, both analytically and numerically, various topological quantities, such the ground state degeneracy, the Chern number and the Hall viscosity.

Self-similarity of spectral response functions for fractional quantum Hall states with long-range interactions

“…We consider a two-dimensional system of N spinpolarized fermions of mass m and charge q in a perpendicular magnetic field B on the xy-plane with periodic boundary conditions. Building on earlier work, 4,[18][19][20] the torus geometry has recently experienced a revival of interest, particularly regarding numerical advances, 6,21 model wavefunctions, 5,[22][23][24] and effective theories, 25,26 which motivates our choice. We consider the Landau gauge such that the momentum k y is a good quantum number.…”