Master-field simulations of O($a$)-improved lattice QCD: Algorithms, stability and exactness

In master-field simulations of lattice QCD, the expectation values of interest are obtained from a single or at most a few representative gauge-field configurations on very large lattices. If the light quarks are included, the generation of these fields using standard techniques is however challenging in view of various algorithmic instabilities and precision issues. Ways to overcome these problems are described here for the case of the O( a )-improved Wilson formulation of lattice QCD and the viability of the proposed measures is then checked in extensive simulations of the theory with 2+1 flavours of quarks.