Coefficients

The core part of the class are the coefficients introduced in Eq. (12) and Eq. (13) in the paper:

\[ \begin{align}\begin{aligned}s_P(n_{P},\lambda)&=\sum_{k=n^{\text{low}}_P}^{n_{P}-1} D_Q(L_P,k)D_Q(\Gamma,n -\lambda-k)\\ f_P(\lambda_P+n_{P}) &= D_Q(\Gamma_P,n-\lambda-n_{P})\end{aligned}\end{align} \]

Here, \(P\) refers to a subsystem and \(D_Q\) is the dimension formula given here. While \(\Gamma_P\) is the remaining length to the left of the subsystem \(P\) and state independent, \(\lambda_P\) is the number of particles (or magnetization) to the right of the subsystem \(P\) and depends on the specific state \(\vert\Psi\rangle\). The coefficient are arranged is non-trivial way optimized for the iteration over a specific state.

\[ \begin{align}\begin{aligned}\lambda_P &=\sum_{T\in\{Q,\dots,Z\}}n_{T}\\\Gamma_P &= L - \sum_{T\in\{Q,\dots,Z\}}L_T\end{aligned}\end{align} \]

std::vector<uint64_t> danceq::internal::BasisU1::offsets

Coefficients defined in Eq. (12) in the paper.

Vector containing all possible coefficients from Eq. (12) in the paper. The maximal size of this vector for a uniform partition is L \(\cdot\) (Q-1) \(\cdot\) n. Elements are arranged in a non-trivial way.

std::vector<uint64_t> danceq::internal::BasisU1::strides

Coefficients defined in Eq. (13) in the paper.

Vector containing all possible coefficients from Eq. (13) in the paper. The maximal size of this vector for a uniform partition is L \(\cdot\) (Q-1). Elements are arranged in a non-trivial way.