Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study

TL;DR

This study extends the Monte Carlo method for composite fermion wavefunctions to cases with negative effective magnetic fields, analyzing ground states and excitations, and confirming results through particle-hole symmetry.

Contribution

The paper generalizes the Jain-Kamilla method to negative effective magnetic fields, enabling analysis of previously inaccessible states with new numerical results.

Findings

Confirmed the correctness of the method via particle-hole symmetry.

Provided ground state energies and excitation spectra for new negative p cases.

Compared results across different m and p values, including unaddressed states.

Abstract

The method of Jain and Kamilla [PRB {\bf 55}, R4895 (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. Finally, we present similar results for ground state energies and low energy neutral excitations for the states with m=2 and p <0 which were not previously addressable, comparing our results to the m=1 case and the p > 0, m=2 cases.