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

Research paper by ** JLQCD Collaboration, S. Aoki, R. Burkhalter, M. Fukugita, S. Hashimoto, K-I. Ishikawa, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, M. Okawa, T. Onogi, S. Tominaga, N. Tsutsui, et al.**

Indexed on: **30 Aug '02**Published on: **30 Aug '02**Published in: **High Energy Physics - Lattice**

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join for free

#### 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.