Directed geometrical worm algorithm applied to the quantum rotor model

TL;DR

This paper introduces a directed geometrical worm algorithm for quantum link-current models, improving efficiency and providing a straightforward way to compute correlation functions, with detailed proofs and results for the quantum rotor model.

Contribution

The paper presents a novel directed worm algorithm with a simple numerical procedure for minimizing erasure probability, applicable to quantum link-current models.

Findings

Reduced auto-correlation times in simulations.

Efficient computation of correlation functions.

Validated algorithm through analytical proofs and numerical results.

Abstract

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part,is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore we show how correlation functions, C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and un-directed geometrical worm algorithms. Results for auto-correlation times and Green functions are presented for the quantum rotor model.