PairDiagSph: Generalization of the exact pairing diagonalization program for spherical systems

We present an efficient program for the exact diagonalization solution of the pairing Hamiltonian in spherical systems with rotational invariance based on the SU(2) quasi-spin algebra. The basis vectors with quasi-spin symmetry considered are generated by using an iterative algorithm. Then the Hamiltonian matrix constructed on this basis is diagonalized with the Lanczos algorithm. All non-zero matrix elements of the Hamiltonian matrix are evaluated “on the fly” by the scattering operator and hash search acting on the basis vectors. The OpenMP parallel program thus developed, PairDiagSph, can efficiently calculate the ground-state eigenvalue and eigenvector of general spherical pairing Hamiltonians. Systems with dimension up to 10^8 can be calculated in few hours on standard desktop computers.

我们提出了一款基于SU(2)准自旋代数（SU(2) quasi-spin algebra）、面向具有旋转不变性的球形体系配对哈密顿量（pairing Hamiltonian）精确对角化求解的高效程序。该程序通过迭代算法生成考虑准自旋对称性的基矢；基于该基矢构建的哈密顿量矩阵可借助兰索斯算法（Lanczos algorithm）完成对角化。哈密顿量矩阵的全部非零矩阵元，均可通过作用于基矢的散射算符与哈希搜索（hash search）实时动态计算。由此开发的OpenMP并行程序PairDiagSph，可高效求解通用球形配对哈密顿量的基态本征值与本征矢。对于维度高达10^8的体系，在标准台式计算机上仅需数小时即可完成计算。