PairDiagSph: Generalization of the Exact Pairing Diagonalization Program for Spherical Systems

TL;DR

PairDiagSph is an efficient, parallelized program that accurately solves the pairing Hamiltonian in spherical systems using SU(2) quasi-spin algebra, enabling large-scale calculations on standard desktops.

Contribution

It introduces a novel, efficient implementation of exact diagonalization for spherical pairing Hamiltonians leveraging SU(2) symmetry and parallel computing.

Findings

Can handle systems with dimension up to 10^8

Calculates ground-state eigenvalues and eigenvectors efficiently

Operates on standard desktop computers within hours

Abstract

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.