Transformation of statistics in fractional quantum Hall systems

A Fermion to Boson transformation is accomplished by attaching to each Ferm ion a tube carrying a single quantum of flux oriented opposite to the appli ed magnetic field. When the mean field approximation is made in Haldane's s pherical geometry, the Fermion angular momentum l(F) is replaced by l(B) = l(F) - (1)/(2) (N - 1). The set of allowed total angular momentum multiplet s is identical in the two different pictures. The Fennion 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 moment um L-12) increases as L-12(L-12 + 1). Similar bands of low energy states oc cur in the two spectra if V increases more quickly than this. (C) 2001 Publ ished by Elsevier Science B.V.