It enables to reduce the number of the free variational parameters $W_p(\theta_j)$ within the TPVF minimization part down to $N_{\rm Heis}^{(p)}$ as listed in table \[Tab1\]. Despite the significant reduction, the number of the free parameters $N_{\rm Heis}^{(p)}$ still grows fast with respect to the increasing lattice parameter $p$. The computational time of the minimization algorithm is significantly prolonged due to (at least) linear dependence on the increasing number of the free variational parameters. Also, the algorithm may possibly be trapped in a local energy minimum and thus a series of initial conditions has to be tested in order to obtain the global energy minimum (or, at least, a sufficiently good approximation of it). For all these reasons, the calculations were stopped at $p=11$ with respect to the constraints of our computational resources and time.

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                   XY          Heisenberg
     $4$      $-1.08456618$   $-1.3089136$
     $5$      $-1.08151200$   $-1.2912704$
     $6$      $-1.08097046$   $-1.2925639$
     $7$      $-1.08086301$   $-1.2918936$
     $8$      $-1.08084068$   $-1.2919769$
     $9$      $-1.08083585$   $-1.2919403$
     $10$     $-1.08083478$   $-1.2919460$
     $11$     $-1.08083453$   $-1.2919437$
   $\infty$   $-1.08083446$   $-1.291944$
  ---------- --------------- --------------

  : The ground-state energies per bond $E_0^{(p)}$ listed with respect to $p$ for the Heisenberg and XY models. The number of block spin states [@White; @Nishino] kept was $m=20$ for 