Path integral Monte Carlo using multigrid techniques

Abstract

Monte Carlo simulations of euclidean path integrals based on local update algorithms are severely hampered by diverging autocorrelation times τ in the continuum limit. If ϵ denotes the discretization parameter we verify for simulations with the standard Metropolis algorithm the theoretically expected behaviour τ∝ (1/ϵ) 2. We then demonstrate numerically that this problem can be overcome by using mathematically very well-founded multigrid techniques.