PairDiag: An exact diagonalization program for solving general pairing Hamiltonians

We present a program for solving exactly the general pairing Hamiltonian based on diagonalization. The program generates the seniority-zero shell-model-like basis vectors via the ‘01’ inversion algorithm. The Hamiltonian matrix is constructed in this seniority-zero space. The program evaluates all non-zero elements of the Hamiltonian matrix “on the fly” using the scattering operator and a search algorithm. The matrix is diagonalized by using the iterative Lanczos algorithm. The OpenMP parallel program thus developed, PairDiag, can efficiently calculate the ground-state eigenvalue and eigenvector of the general pairing Hamiltonian for both the even-mass and the odd-mass system. The program is packaged in a Fortran module, which makes it easy to use the program to replace the BCS approximation in standard self-consistent mean field calculations. For systems with dimension around 10^8, the calculation can be done within hours on standard desktop computers.本研究提出一款基于对角化方法精确求解广义配对哈密顿量（general pairing Hamiltonian）的程序。该程序通过‘01’反演算法生成零资历数（seniority-zero）类壳模型基矢，哈密顿量矩阵即在该零资历数空间中构建。本程序借助散射算子与搜索算法，实时（on the fly）计算哈密顿量矩阵的全部非零元，并通过迭代兰索斯（Lanczos）算法实现矩阵对角化。由此开发的基于OpenMP的并行程序PairDiag，可高效计算偶质量与奇质量体系下广义配对哈密顿量的基态本征值与本征矢。本程序以Fortran模块形式封装，可便捷地在标准自洽平均场计算中替代巴丁-库珀-施里弗（BCS）近似。对于维度约为10^8的体系，在标准台式计算机上即可在数小时内完成计算。