Constructing Composite Fermion Fermi Liquid States with "Squeezed" Jain States*

We consider the composite fermion Fermi liquid (CFFL) state on the spherical geometry. We construct the CFFL wave functions from those of Jain states by requiring the flux in the two cases to be equal (aliasing). We use the squeezing rules of Regnault, Bernevig and Haldane (RBH) to obtain the appropriate truncated basis of squeezed states. We obtain the Jain states by diagonalizing the angular momentum operator in the truncated basis, as prescribed by RBH. We study the Read-Rezayi (RR) CFFL state for N=9 in two ways: directly from the (N=9, ν=3/7) Jain state, and from particle-hole (P-H) conjugations of the (N=8, ν=2/5) Jain state. Similar considerations apply to the (N=15, ν=3/7) Jain state and its P-H conjugate for the N=16 CFFL filled shell Fermi sea. We also consider N=12 as a case of a P-H symmetric CFFL (which is aliased with the (N=12, ν=3/7) Jain state) and measure the degree of its P-H symmetry. We note that none of the states past N=9 can feasibly be obtained from the method used by RR, which involves O(N!) complexity. Whenever appropriate we compare our construction to the Kamilla-Jain determinant form of the states.