[@DaniskaGendiar]. Thus, in case of a system with the rotational and the spin-ordering symmetry (as in the TFIM), there are only $N_{\rm Ising}^{(p)}$ free variational parameters $W_p(\theta_j)$ within the set of $2^p$ tensor elements $W_p(\{\sigma\})$. If there is no preferred spin alignment in the system (such as in the XY model, the Heisenberg model, as well as in the TFIM at and above the phase transition magnetic field), the spin-inversion symmetry appears. For instance, if $p=4$, the configuration $\{{\uparrow}{\uparrow}{\uparrow}{\downarrow}\}$ is equivalent to $\{{\downarrow}{\downarrow}{\downarrow}{\uparrow}\}$, which is obtained by flipping each spin. Such an additional symmetry results in consequent reduction of the set of the free variational parameters, the size of which drops to $N_{\rm Heis}^{(p)} < N_{\rm Ising}^{(p)}$. The numbers of the free variational parameters $N_{\rm Ising}^{(p)}$ and $N_{\rm Heis}^{(p)}$ with respect to the lattice parameter $p$ are summarized in table \[Tab1\]. In addition, one more variational parameter can be eliminated from each set of the free variational parameters by setting it to $1$, being the normalization condition in $W_p(\{\sigma\})$ and $| \Psi_p \rangle$, consequently.

                 $p$                   $4$   $5$    $6$    $7$    $8$    $9$   $10$    $11$
  ---------------------------------- ----- ----- ------ ------ ------ ------ ------ -------
         $N_{\rm Heis}^{(p)}$          $4$   $4$    $8$    $9$   $18$   $23$   