Symmetry¶
Constraints Fock space → FCI space¶
Molecular system determines satisfy:
\[\begin{split}\begin{equation}
\begin{split}
n_{\alpha} + n_{\beta} & = n_e \\
n_{\alpha} - n_{\beta} & = C \\
\end{split}
\end{equation}\end{split}\]
the configuration \(x \in \{0, 1\}^{N}\), (1: occupied, 0: unoccupied, N: spin-orbitals),
k-th spin-orbitals satisfy:
\[\begin{split}\begin{equation}
\begin{split}
n_{\alpha} - \left(\frac{N}{2} - k//2\right) &
\leq n_{\uparrow} = \sum_{j=0}^{k//2}x_{2j} \leq n_{\alpha} \\
n_{\beta} - \left(\frac{N}{2} - k//2\right) &
\leq n_{\downarrow} = \sum_{j=0}^{k//2}x_{2j+1} \leq n_{\beta} \\
\end{split}
\end{equation}\end{split}\]
so, when k is even number (\(n_{\uparrow} \textbf{dose not include}\) k-th spin-orbitals for sampling convenience):
\[\begin{equation}
n_{\alpha} - \left(\frac{N}{2} - k//2\right) < n_{\uparrow} \quad n_{\alpha} > n_{\uparrow} \label{cond1}
\end{equation}\]
when k is old number (\(n_{\downarrow} \textbf{dose not include}\) k-th spin-orbitals for sampling convenience):
\[\begin{equation}
n_{\beta} - \left(\frac{N}{2} - k//2\right) < n_{\downarrow} \quad n_{\beta} > n_{\downarrow} \label{cond2}
\end{equation}\]
- see:
vmc/ansatz/utils/symmetry_mask
Exclude partial dets¶
Using Binary Search to exclude partial dets
- see:
vmc/ansatz/utils/orthonormal_maskanddocs/remove-det.pdf