and restricting the Hilbert space to the sector that preserves the total spin projection, S z . To implement in addition the H SVOC coupling, one needs to remove all restrictions on S z and V z when building the basis of Slater determinants. This requires substantially larger Hilbert spaces, e.g., for the case of K = 54 employed in the calculations of Fig. , the dimension of the Hilbert space (the master index I) increases from 5778 (using an S z = 0 restriction only) to 23220 basis Slater determinants (with no S z and V z restrictions).