Tempered Fermions in the Hybrid Monte Carlo Algorithm

The standard algorithms used for full QCD are painfully slow. Physically large objects, like instantons, pions etc., may well decorrelate much more slowly than, say, the plaquette [1]. Tempered algorithms [1–3] promote a parameter of the theory to a dynamical variable that changes during the simulation, which has tremendous potential for speeding up slow simulations. They have been successfully implemented in β for spin glasses, U(1) etc. For QCD at zero temperature promoting β does not help (although at high temperature, around the chiral phase transition it probably will), but promoting the quark mass, and allowing it to change during the simulation, does speed things up. The mass is only changed if the configuration is simultaneously in the equilibrium distribution of both masses. So tempering is always in equilibrium and requires no re-weighting etc. afterwards. The minimum gain comes from running at heavier (faster) masses between independent configurations. The maximum gain comes if the relevant auto-correlations are smaller for larger masses.