Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

TL;DR

This paper introduces optimized methods for Hybrid Monte Carlo simulations of the Hubbard model on hexagonal lattices, achieving over tenfold speed improvements through advanced solver techniques and automated parameter tuning.

Contribution

It presents a novel combination of solver and integrator optimizations, along with an automated tuning algorithm for Hasenbusch mass parameters, enhancing simulation efficiency.

Findings

Over tenfold speedup with Hasenbusch acceleration

Excellent agreement with direct diagonalization benchmarks

Effective automated tuning of Hasenbusch masses

Abstract

We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to $102\times 102$ and $N_t=64$. We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.