A Study of Parallelizing O(N) Green-Function-Based Monte Carlo Method for Many Fermions Coupled with Classical Degrees of Freedom

TL;DR

This paper explores the parallelization of the O(N) Green-Function-Based Monte Carlo method for many fermions with classical degrees of freedom, demonstrating significant performance improvements using GPU and CPU clusters.

Contribution

It implements and evaluates the parallelization of the GFMC method on GPU and CPU clusters, showing enhanced performance for large Hamiltonian matrices.

Findings

GPU implementation outperforms 30 CPU cores for a 32^3 Hamiltonian

Parallel scaling improves with increased nodes and matrix size

GPU-based GFMC achieves higher efficiency than CPU-based methods

Abstract

Models of fermions interacting with classical degrees of freedom are applied to a large variety of systems in condensed matter physics. For this class of models, Wei{\ss}e [Phys. Rev. Lett. {\bf 102}, 150604 (2009)] has recently proposed a very efficient numerical method, called O($N$) Green-Function-Based Monte Carlo (GFMC) method, where a kernel polynomial expansion technique is used to avoid the full numerical diagonalization of the fermion Hamiltonian matrix of size $N$, which usually costs O($N^3$) computational complexity. Motivated by this background, in this paper we apply the GFMC method to the double exchange model in three spatial dimensions. We mainly focus on the implementation of GFMC method using both MPI on a CPU-based cluster and Nvidia's Compute Unified Device Architecture (CUDA) programming techniques on a GPU-based (Graphics Processing Unit based) cluster. The time complexity of the algorithm and the parallel implementation details on the clusters are discussed. We also show the performance scaling for increasing Hamiltonian matrix size and increasing number of nodes, respectively. The performance evaluation indicates that for a $32^3$ Hamiltonian a single GPU shows higher performance equivalent to more than 30 CPU cores parallelized using MPI.