Dynamical fermions as a global correction

TL;DR

This paper introduces a family of exact algorithms for simulating dynamical fermions in the Schwinger model, utilizing stochastic determinant estimates and eigenvalue analysis to improve acceptance rates across various parameters.

Contribution

It develops new algorithms combining stochastic estimates and eigenvalue exploitation to efficiently simulate dynamical fermions with high acceptance rates.

Findings

Achieved high acceptance rates with large proposed steps

Effective simulation across a range of couplings and masses

Utilized eigenvalues for improved determinant ratio estimation

Abstract

In the simplified setting of the Schwinger model we present a systematic study on the simulation of dynamical fermions by global accept/reject steps that take into account the fermion determinant. A family of exact algorithms is developed, which combine stochastic estimates of the determinant ratio with the exploitation of some exact extremal eigenvalues of the generalized problem defined by the `old' and the `new' Dirac operator. In this way an acceptable acceptance rate is achieved with large proposed steps and over a wide range of couplings and masses.