Application of Domain Decomposition to the Evaluation of Fermion Determinant Ratios

TL;DR

This paper investigates the use of domain decomposition for estimating fermion determinant ratios in mass reweighting of Wilson fermions, analyzing fluctuations and proposing a stochastic estimation method for single-flavor cases.

Contribution

It introduces a domain decomposition approach to evaluate fermion determinant ratios and a stochastic method for one flavor without square root approximation, improving reweighting efficiency.

Findings

Fluctuations depend on volume and mass shift

Method estimates reweighting cost and effectiveness

Proposes a new stochastic estimation for single flavor

Abstract

We analyze the fluctuations in the case of mass reweighting for N_f=2 Wilson fermions. We use a domain decomposition factorization of the fermion determinant. Ratios of determinants are estimated stochastically. We study the stochastic and the ensemble fluctuations as a function of the volume V and the mass shift Delta m. With our result it is possible to estimate the cost and the effectiveness of mass reweighting. In addition we introduce a stochastic estimation for the one flavor case without using the square root.