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

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.

arXiv commentCorrected Proof in Press in Computer Physics Communications

References in corpus (24)

• The NumPy array: a structure for efficient numerical computation
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• Density waves and Cooper pairing on the honeycomb lattice
• Lattice field theory simulations of graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• HMC algorithm with multiple time scale integration and mass preconditioning
• Optimized Verlet-like algorithms for molecular dynamics simulations
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• The 2D Hubbard model on the honeycomb lattice
• Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study
• Antiferromagnetism of the Hubbard Model on a Layered Honeycomb Lattice - Is MgB${}_2$ a Nearly-Antiferromagnetic Metal? -
• Quantum Monte Carlo Calculations for Carbon Nanotubes
• Topological Aspects of Fermions on a Honeycomb Lattice
• Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions
• Path integral representation for the Hubbard model with reduced number of Lefschetz thimbles
• Applications of lattice QCD techniques for condensed matter systems
• Hybrid Monte Carlo Simulation of Graphene on the Hexagonal Lattice
• Improving DWF Simulations: the Force Gradient Integrator and the Möbius Accelerated DWF Solver

Cited by in corpus (10)

• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice
• Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• A density of states approach to the hexagonal Hubbard model at finite density
• The Ising Model with Hybrid Monte Carlo
• On the Infinite Variance Problem in Fermion Models
• Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration
• The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Stochastic and Tensor Network simulations of the Hubbard Model