Sampling of General Correlators in Worm Algorithm-based Simulations

Abstract

Using the complex $\phi^4$-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator $<\phi^{*}(x)\phi(y)>$, but also more general correlators such as $<|\phi(x)||\phi(y)|>$ or $<\text{arg}(\phi(x))\text{arg}(\phi(y))>$, as well as condensates like $<|\phi|>$, 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.