Directed geometrical worm algorithm applied to the quantum rotor model

Fabien Alet and Erik S. Sørensen
Phys. Rev. E 68, 026702 – Published 12 August 2003
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Abstract

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm the 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,τ) can be straightforwardly obtained from the probability of a worm to reach a site (r,τ) 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 undirected geometrical worm algorithms. Results for autocorrelation times and Green’s functions are presented for the quantum rotor model.

  • Received 24 February 2003

DOI:https://doi.org/10.1103/PhysRevE.68.026702

©2003 American Physical Society

Authors & Affiliations

Fabien Alet1,2,* and Erik S. Sørensen3

  • 1Computational Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland
  • 2Theoretische Physik, ETH Zürich, CH-8093 Zürich, Switzerland
  • 3Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1

  • *Electronic address: alet@phys.ethz.ch

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Vol. 68, Iss. 2 — August 2003

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