Parallelization of the exact diagonalization of the t-t'-Hubbard model

TL;DR

This paper introduces a parallel algorithm for exact diagonalization of the $t-t'$-Hubbard model, achieving significant speedups and enabling detailed studies of the model's ground state properties and correlation functions.

Contribution

A novel parallel algorithm with a new state labeling scheme for the $t-t'$-Hubbard model's exact diagonalization, improving computational efficiency.

Findings

Achieved up to fourfold speedup on 16 nodes for ground state energy calculations.

Obtained nearly linear speedup for correlation function computations.

Studied the impact of $t'$ on ground state energy and superconducting correlations.

Abstract

We present a new parallel algorithm for the exact diagonalization of the $t-t'$-Hubbard model with the Lanczos-method. By invoking a new scheme of labeling the states we were able to obtain a speedup of up to four on 16 nodes of an IBM SP2 for the calculation of the ground state energy and an almost linear speedup for the calculation of the correlation functions. Using this algorithm we performed an extensive study of the influence of the next-nearest hopping parameter $t'$ in the $t-t'$-Hubbard model on ground state energy and the superconducting correlation functions for both attractive and repulsive interaction.