Exact results for the spectra of interacting bosons and fermions on the lowest Landau level
Abstract
A system of N interacting bosons or fermions in a twodimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for the matrix elements of any interaction, in the basis of angular momentum eigenstates. For the fermion ‘ground state’ (ν = 1 Laughlin state), this makes it possible to exactly calculate its energy all the way up to the mesoscopic regime N ∼ 1000. It is also shown that for N = 3 and Coulomb interaction, several rational lowlying values of energy exist, for bosons and fermions alike.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 February 2013
 DOI:
 10.1088/17425468/2013/02/P02013
 Bibcode:
 2013JSMTE..02..013M