Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2000-07-28
Physica E 9, 701 (2001)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
5 pages, 4 figures, submitted to Physica E
Scientific paper
10.1016/S1386-9477(00)00293-9
A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B= l_F-{1\over2}(N-1)$. 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 if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.
Benjamin Arthur
Quinn Jennifer J.
Quinn John J.
Wojs Arkadiusz
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