Remarks on the construction of worm algorithms for lattice field theories in worldline representation

Abstract

We introduce a generalized worldline model where the partition function is a sum over configurations of a conserved flux on a d-dimensional lattice. The weights for the configurations of the corresponding worldlines have factors living on the links of the lattice, as well as terms which live on the sites x and depend on all fluxes attached to x. The model represents a general class of worldline systems, among them the dual representation of the relativistic Bose gas at finite density. We construct a suitable worm algorithm and show how to correctly distribute the site weights in the various Metropolis probabilities that determine the worm. We analyze the algorithm in detail and give a proof of detailed balance. Our algorithm admits the introduction of an amplitude parameter A that can be chosen freely. Using a numerical simulation of the relativistic Bose gas we demonstrate that A allows one to influence the starting and terminating probabilities and thus the average length and the efficiency of the worm.

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