Sampling of general correlators in worm-algorithm based simulations

Using the complex ϕ4ϕ4-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator 〈ϕ⁎(x)ϕ(y)〉〈ϕ⁎(x)ϕ(y)〉, but also more general correlators such as 〈|ϕ(x)||ϕ(y)|〉〈|ϕ(x)||ϕ(y)|〉 or 〈arg⁡(ϕ(x))arg⁡(ϕ(y))〉〈arg⁡(ϕ(x))arg⁡(ϕ(y))〉, as well as condensates like 〈|ϕ|〉〈|ϕ|〉, can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models.