标题： 基于图的全组态相互作用哈密顿量的块对角化：H$_2$链研究 显示英文标题

标题： Graph-based block-diagonalization of full configuration interaction Hamiltonian: H$_2$ chains study

摘要： 我们开发了一种基于图的块对角化（GBBD）方法，用于分子系统的全组态相互作用哈密顿量，以高效计算低能态的精确本征值。 在此方法中，哈密顿量的非零矩阵元被表示为图上的边，该图自然分解为不相连的簇。 每个簇对应于哈密顿量块对角化形式中的一个独立块。 通过求解每个块矩阵的本征值问题，并在相对于之前计算的低能本征态满足正交性约束条件下求解修改后的哈密顿量，获得了低能区域的本征值。 我们将GBBD方法应用于从H$_2$到H$_{12}$的线性氢链。 结果与精确结果高度一致，证实了所提出方法的准确性和效率。 最后，我们讨论了与H$_2$分子数量相关的几种物理性质。 显示英文摘要

摘要： We developed a graph-based block-diagonalization (GBBD) method for the full configuration interaction Hamiltonian of molecular systems to efficiently calculate the exact eigenvalues of low-energy states. In this approach, the non-zero matrix elements of the Hamiltonian are represented as edges on a graph, which naturally decomposes into disconnected clusters. Each cluster corresponds to an independent block in the block-diagonalized form of the Hamiltonian. The eigenvalues in the low-energy sector were obtained by solving the eigenvalue problem for each block matrix and by solving a modified Hamiltonian subject to orthonormality constraints with respect to previously computed lower-energy eigenstates. We applied the GBBD method to linear hydrogen H chains ranging from H$_2$ to H$_{12}$. The results showed excellent agreement with exact ones, confirming both the accuracy and efficiency of the proposed method. Finally, we discussed several physical properties with respect to the number of H$_2$ molecules.