Dynamical tuning of the chemical potential in grand canonical Monte Carlo simulations to achieve target particle number

Here we discuss a method to adjust the chemical potential in grand canonical ensemble Monte Carlo simulations to achieve a target mean particle number that was recently introducted in Phys. Rev. E 105, 045311. The method applies a fictitious dynamics to the chemical potential that runs concurrently with the Monte Carlo sampling of the physical system. The resulting corrections to the chemical potential are made according to time-averaged estimates of the mean and variance of the particle number, with the latter being proportional to thermodynamic compressibility. We present results for a variety of tests, both within the context of classical and quantum Monte Carlo simulations, and in all cases find rapid convergence of the chemical potential---inexactness of the tuning algorithm contributes only a minor part of the total measurement error for realistic simulations.