Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum IF is replaced by IB = IF - $(N - 1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum Ll2) increases as LI2(Ll2 + 1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this. @ 2001 Published by Elsevier Science B.V.