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

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 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 moderately large lattice size ($16^{3}\times 48$) with intermediate quark masses ($m_{\mathit{PS}}/m_{\mathit{V}}\sim 0.7$-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 to those of the established algorithms for $N_f=2$ QCD. These tests establish that our PHMC algorithm works on moderately large lattice sizes with intermediate quark mass ($16^{3}\times 48, m_{\mathit{PS}}/m_{\mathit{V}}\sim 0.7$-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 agreement of results with those obtained with the R algorithm and extrapolated to zero molecular dynamics step size.