Toward large-scale Hybrid Monte Carlo simulations of the Hubbard model on graphics processing units

TL;DR

This paper demonstrates significant speedups in Hybrid Monte Carlo simulations of the Hubbard model by leveraging GPU acceleration, enabling more efficient large-scale quantum many-body system studies.

Contribution

It provides a detailed performance comparison of sparse matrix-vector multiplication on CPU and GPU for the Hubbard model, highlighting substantial computational gains.

Findings

Speedup factors of 30-350 for d=1

Speedup factors over 40 for d=3

GPU implementation greatly enhances large-scale simulations

Abstract

The performance of the Hybrid Monte Carlo algorithm is determined by the speed of sparse matrix-vector multiplication within the context of preconditioned conjugate gradient iteration. We study these operations as implemented for the fermion matrix of the Hubbard model in d+1 space-time dimensions, and report a performance comparison between a 2.66 GHz Intel Xeon E5430 CPU and an NVIDIA Tesla C1060 GPU using double-precision arithmetic. We find speedup factors ranging between 30-350 for d = 1, and in excess of 40 for d = 3. We argue that such speedups are of considerable impact for large-scale simulational studies of quantum many-body systems.