Polynomial Hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors

Abstract

We present a polynomial hybrid Monte Carlo (PHMC) algorithm for lattice QCD with odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm makes use of the non-Hermitian Chebyshev polynomial to approximate the inverse square root of the fermion matrix required for an odd number of flavors. The systematic error from the polynomial approximation is removed by a noisy Metropolis test for which a new method is developed. Investigating the property of our PHMC algorithm in the N_f=2 QCD case, we find that it is as efficient as the conventional HMC algorithm for a moderately large lattice size (16^3 times 48) with intermediate quark masses (m_{PS}/m_V ~ 0.7-0.8). We test our odd-flavor algorithm through extensive simulations of two-flavor QCD treated as an N_f = 1+1 system, and comparing the results with those of the established algorithms for N_f=2 QCD. These tests establish that our PHMC algorithm works on a moderately large lattice size with intermediate quark masses (16^3 times 48, m_{PS}/m_V ~ 0.7-0.8). Finally we experiment with the (2+1)-flavor QCD simulation on small lattices (4^3 times 8 and 8^3 times 16), and confirm the agreement of our results with those obtained with the R algorithm and extrapolated to a zero molecular dynamics step size.

arXiv comment58 pages, LaTeX2e with RevTeX4, v2: typos corrected, published version

References in corpus (29)

• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• O(a) improvement of lattice QCD with two flavors of Wilson quarks
• A New Approach to the Problem of Dynamical Quarks in Numerical Simulations of Lattice QCD
• Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized Biconjugate Gradient Algorithm
• A Polynomial Hybrid Monte Carlo Algorithm
• First results on the running coupling in QCD with two massless flavours
• The Deconfinement Phase Transition in One-Flavour QCD
• Systematic errors of Lüscher's fermion method and its extensions
• Fast Fermion Monte Carlo
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• A Noisy Monte Carlo Algorithm
• Implementation of Symanzik's Improvement Program for Simulations of Dynamical Wilson Fermions in Lattice QCD
• The PHMC algorithm for simulations of dynamical fermions: I -- description and properties
• Instability in the Molecular Dynamics Step of Hybrid Monte Carlo in Dynamical Fermion Lattice QCD Simulations
• Non-hermitian Exact Local Bosonic Algorithm for Dynamical Quarks
• UV-filtered fermionic Monte Carlo
• Choice of Integrator in the Hybrid Monte Carlo Algorithm
• Quadratically optimized polynomials for fermion simulations
• Comparative Benchmarks of full QCD Algorithms
• The PHMC algorithm for simulations of dynamical fermions: II - Performance analysis
• Instabilities and Non-Reversibility of Molecular Dynamics Trajectories
• Light hadron spectroscopy with two flavors of O(a) improved dynamical quarks
• Molecular dynamics for full QCD simulations with an improved action
• Liapunov Exponents and the Reversibility of Molecular Dynamics Algorithms
• Simulation of n_f =3 QCD by Hybrid Monte Carlo
• Efficiency of the UV-filtered Multiboson algorithm
• Numerical simulation of dynamical gluinos: experience with a multi-bosonic algorithm and first results
• Ordering monomial factors of polynomials in the product representation
• Improved Multiboson Algorithm

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• Lattice QCD with two dynamical flavors of domain wall quarks
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• Nonperturbative $O(a)$ improvement of the Wilson quark action with the RG-improved gauge action using the Schrödinger functional method
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• $I=2$ $\pi \pi$ scattering phase shift from the HAL QCD method with the LapH smearing
• $I=2$ $\pi \pi$ potential in the HAL QCD method with all-to-all propagators
• Non-perturbative improvement of the axial current with three dynamical flavors and the Iwasaki gauge action
• Higher Order Hybrid Monte Carlo at Finite Temperature
• Symanzik improvement of lattice QCD with four flavors of Wilson quarks
• An Exact Algorithm for Any-flavor Lattice QCD with Kogut-Susskind Fermion
• Hadron Spectrum from Dynamical Lattice QCD Simulations
• An application of the UV-filtering preconditioner to the Polynomial Hybrid Monte Carlo algorithm
• Recent algorithm and machine developments for lattice QCD
• Three flavor dynamical QCD project by CP-PACS/JLQCD
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