Sampling of General Correlators in Worm Algorithm-based Simulations

TL;DR

This paper introduces a method to measure a variety of correlators and condensates during worm algorithm simulations of the complex -model, enabling more comprehensive data collection at each Monte Carlo step.

Contribution

The authors present a novel approach to measure multiple correlators and condensates during worm algorithm simulations, extending the capabilities beyond traditional closed-worm configurations.

Findings

Correlators like (x)(y) and (||) can be measured at each step.

The method applies to other models such as spin and sigma models.

Enhanced data collection improves simulation efficiency and analysis.

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.