Exact diagonalization of the Hubbard model on graphics processing units

TL;DR

This paper demonstrates that implementing the exact diagonalization of the Hubbard model on GPUs significantly accelerates computations, achieving over 100x speedups compared to CPU implementations in both 1D and 2D cases.

Contribution

The paper introduces a GPU-based implementation of the exact diagonalization method for the Hubbard model, providing substantial performance improvements over traditional CPU codes.

Findings

Speedups of over 100x in 1D case

Speedups of over 110x in 2D case

Effective use of Lanczos algorithm on GPU

Abstract

We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a one-dimensional ring and a two-dimensional square lattice. In the one-dimensional case, we obtain speedups of over 100 and 60 in single and double precision arithmetic, respectively. In the two-dimensional case, the corresponding speedups are over 110 and 70.