Padé-[Formula presented] estimator of determinants

C. Thron, S. J. Dong, K. F. Liu, H. P. Ying

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


We introduce the Padé-(Formula presented) (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 (Formula presented) 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.

Original languageEnglish
Pages (from-to)1642-1653
Number of pages12
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number3
StatePublished - 1998

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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