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 10⁸ can be calculated in few hours on standard desktop computers.

Program summary

Program Title: PairDiagSph.

CPC Library link to program files: https://doi.org/10.17632/n54vr2kwx8.1

Code Ocean capsule: https://codeocean.com/capsule/9159628

Licensing provisions: CC by NC 3.0.

Programming language: Fortran 95.

Nature of problem: The exact diagonalization of spherical pairing Hamiltonian can be achieved in the quasi-spin space.

Solution method: The program generates the basis vectors via the adjacency excitation algorithm, and diagonalizes the spherical pairing Hamiltonian by the Lanczos + QR algorithm.

Additional comments including restrictions and unusual features: The total number of spherical must be less than 64; The maximal dimension that can be handled is restricted by the local RAM capacity.

中文翻译：

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PairDiagSph：球形系统精确配对对角化程序的推广

我们提出了一个基于SU（2）准自旋代数的球面系统中具有旋转不变性的成对哈密顿量的精确对角化解决方案的有效程序。通过使用迭代算法来生成具有准自旋对称性的基本向量。然后，用Lanczos算法将在此基础上构造的哈密顿矩阵对角化。哈密​​顿矩阵的所有非零矩阵元素均由散射算子和基于基矢量的哈希搜索“动态”评估。这样开发的OpenMP并行程序PairDiagSph可以有效地计算一般球形配对哈密顿量的基态特征值和特征向量。尺寸最大为10 ^8的系统 在标准台式计算机上可以在几个小时内计算出。

计划摘要

程序标题： PairDiagSph。

CPC库链接到程序文件： https : //doi.org/10.17632/n54vr2kwx8.1

Code Ocean太空舱： https : //codeocean.com/capsule/9159628

许可条款： CC by NC 3.0。

编程语言：Fortran 95。

问题的性质：球形配对哈密顿量的精确对角线化可以在准自旋空间中实现。

解决方法：该程序通过邻接激励算法生成基矢量，并通过Lanczos + QR算法对角线对哈密顿量进行对角化。

其他注释，包括限制和异常特征：球形的总数必须少于64个；球形的总数必须小于64个。可以处理的最大尺寸受本地RAM容量的限制。