15 TABLE VII: RVM-diagonalization total energies [in units of g/ ( π Λ $^{2}$)], relative errors, and overlaps at each intermediate step for the case of the yrast state for N = 5 LLL bosons with L = 8 (see Sec. III D). The notation for the RVM functions is the same as in Eq. (51). The composition of each step is shown in the second column. The last row displays the corresponding quantities for the Moore-Read function [Eq. (50)]. TABLE VIII: RVM-diagonalization total energies [in units of e $^{2}$/ ( κl B )], relative errors, and overlaps at each intermediate step for the case of the yrast state for N = 4 LLL electrons with L = 18 (see Sec. III C). The notation for the RVM functions is the same as in Eq. (46). The composition of each step is shown in the second column. The last row displays the corresponding quantities for the Laughlin function [Eq. (48)]. Step Composition Energy Relative error (%) Overlap 1 | 1 〉 1 . 3964006 (RVM) 17 . 5 0 . 788 2 | 1 〉 + | 3 〉 1 . 2071388 (RVM) 1 . 6 0 . 990 3 | 1 〉 + | 3 〉 + | 2 〉 1 . 1947104 (RVM) 0 . 500 0 . 997 4 | 1 〉 + | 3 〉 + | 2 〉 + | 4 〉 1 . 1884821 (RVM) 0 . 02 0 . 9998 5 | 1 〉 + | 3 〉 + | 2 〉 + | 4 〉 + | 5 〉 1 . 1882199 (RVM) 0 . 00 1 . 000 MOORE-READ 1 . 2658991 6 . 5 0 . 913 Step Composition Energy Relative error (%) Overlap 1 | 1 〉 1 . 3217670 (RVM) 1 . 23 0 . 929 2 | 1 〉 + | 5 〉 1 . 3174550 (RVM) 0 . 90 0 . 961 3 | 1 〉 + | 5 〉 + | 7 〉 1 . 3081859 (RVM) 0 . 19 0 . 992 4 | 1 〉 + | 5 〉 + | 7 〉 + | 2 〉 1 . 3059258 (RVM) 0 . 015 0 . 99965 5 | 1 〉 + | 5 〉 + | 7 〉 + | 2 〉 + | 6 〉 1 . 3058052 (RVM) 0 . 006 0 . 99988 6 | 1 〉 + | 5 〉 + | 7 〉 + | 2 〉 + | 6 〉 + | 4 〉 1 . 3057413 (RVM) 0 . 001 0 . 99997 7 | 1 〉 + | 5 〉 + | 7 〉 + | 2 〉 + | 6 〉 + | 4 〉 + | 3 〉 1 . 3057290 (RVM) 0 . 000 1 . 00000 JASTROW-LAUGHLIN 1 . 3105953 0 . 37 0 . 979 of LLL bosons to mean-field GP behavior for large N , is of high importance conceptually and practically, and we expect that it will be the focus of future experimental and theoretical studies [66]. The fast-convergence properties of the RVM basis can be seen through a tabulation of the intermediate RVM- diagonalization total energies as the size of the RVM basis increases in successive steps. In TABLE VII, in addition to these intermediate RVM energies, we also display the corresponding relative error (relative to the EXD result) and the corresponding overlap with the EXD wave func- tion for the yrast state (denoted by the index [1] in Sec. III D). We stress that convergence (as a function of the num- ber of the RVM basis functions used in the calculation) is seen from TABLE VII to be achieved rapidly (i.e., al- ready with the use of only two basis functions one obtains a relative error of 1.6% for the energy eigenvalue, and a 99% overlap with the exact eigenfunction). In particular, we note that at the second step the RVM wavefunction is already more accurate compared to the Moore-Read function which exhibits a relative error of 6.5% for the energy and an overlap of 91.3% [see TABLE VII]. Acknowledgments 2. The example of N = 4 electrons In this section, we analyze in detail the convergence properties of the RVM diagonalization for the yrast state of N = 5 bosons with L = 8 (a case associated with a Moore-Read function) that was discussed in Sec. III D. In Table VI, we display the coupling matrix elements for the contact interaction between the RVM basis func- tions given in Eq. (51). The convergence properties in the RVM basis cannot be immediately seen from an in- spection of these coupling matrix elements; while most of the off-diagonal elements in TABLE VI are smaller than the differences between the associated diagonal elements, a couple of them are indeed larger. In this section, we analyze in detail the convergence properties of the RVM diagonalization for the yrast state of N = 4 electrons with L = 18 (a case associated with a Jastrow-Laughlin function) that was discussed in Sec. III C. As previously, the convergence properties of the RVM 1. The example of N = 5 bosons Appendix A: Convergence in the RVM basis This work was supported by the U.S. DOE (FG05- 86ER45234).