Composite Fermions in Negative Effective Magnetic Field

The method of Jain and Kamilla [PRB {bf 55}, R4895-R4898 (1997)] allows numerical generation of composite fermion trial wavefunctions for large numbers of electrons in high magnetic fields at filling fractions of the form $nu=p/(2mp+1)$ with $m$ and $p$ positive integers. In the current paper we generalize this method to the case where the composite fermions are in an effective (mean) field with opposite sign from the actual physical field, i.e. when $p$ is negative. We examine both the ground state energies and the low energy neutral excitation spectra of these states. Using particle-hole symmetry we can confirm the correctness of our method by comparing results for the series $m=1$ with $p>0$ (previously calculated by others) to our results for the conjugate series $m=1$ with $p 0$, $m=2$ cases.