Padé-Z2estimator of determinants

Abstract

We introduce the Padé-Z 2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the 8 3 × 12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

Study of stochastic estimates of quark loops with unbiased subtraction

“…For disconnected loop calculation A will be replaced by the inverse fermion matrix M −1 . Previously it was shown that the above variance for M −1 can be reduced substantially [8,2,3,5] by using a set of traceless matrices obtained from the hoping parameter expansion of the fermion matrix M as…”

“…It has been demonstrated that Z 2 noise [6] is the optimal noise with minimum variance [7]. For a given L number of Z 2 noises, variance of this estimation is given by [6,7,8] …”

“…This variance can further be reduced by the method of unbiased subtraction [8], where a set of P traceless matrices (Q) are subtracted from the matrix A as…”

“…They used random noises to estimate various traces involving fermion matrix. Using a set of random noise vectors η, one can estimate the trace of a N × N matrix A as [6,7,8] …”

Sea Contributions to the Electric Polarizability of Hadrons using Reweighting

“…The leading terms in the HPE approximate the neardiagonal behavior of the operators, and the variance in the stochastic estimate of Tr O is equal to the sum of all off-diagonal elements of O. By subtracting an approximation of these terms from the estimator the variance can be reduced [11]. The exact traces of these operators can be calculated analytically since they consist of finite numbers of hops [7]; we have computed them up to 7 th order in κ.…”