# Implementation of Symanzik's Improvement Program for Simulations of Dynamical Wilson Fermions in Lattice QCD

## TL;DR

This paper details implementing Symanzik's improvement in lattice QCD simulations with dynamical Wilson fermions, showing minimal overhead and maintaining standard preconditioning techniques.

## Contribution

It introduces a practical implementation of Sheikholeslami-Wohlert term within the Symanzik improvement framework for dynamical Wilson fermions in lattice QCD.

## Key findings

- Overhead increases by about 20% when CG iterations exceed 200
- Standard even-odd preconditioning remains effective
- Implementation validated through analytical and numerical tests

## Abstract

We discuss the implementation of a Sheikholeslami-Wohlert term for simulations of lattice QCD with dynamical Wilson fermions as required by Symanzik's improvement program. We show that for the Hybrid Monte Carlo or Kramers equation algorithm standard even-odd preconditioning can be maintained. We design tests of the implementation using analytically and numerically computed cumulant expansions. We find that, for situations where the average number of Conjugate Gradient iterations exceeds 200, the overhead is only about 20%.