Residual interactions and correlations among Laughlin quasiparticles:   Novel hierarchy states
  The residual interactions between Laughlin quasiparticles can be obtained from exact numerical diagonalization studies of small systems. The pseudopotentials V_QP(R)$ describing the energy of interaction of QE's (or QH's) as a function of their "relative angular momentum" R cannot support Laughlin correlations at certain QP filling factors (e.g., nu_QE}=1/3 and nu_QH=1/5). Because of this the novel condensed quantum fluid states observed at nu=4/11, 4/13 and other filling fractions cannot possibly be spin polarized Laughlin correlated QP states of the composite Fermion hierarchy. Pairing of the QP's clearly must occur, but the exact nature of the incompressible ground states is not completely clear. 
John J. Quinn, Arkadiusz Wojs, Kyung-Soo Yi