Overlap of the Wilson loop with the broken-string state

TL;DR

The paper demonstrates that detecting string-breaking via Wilson loops is inherently difficult due to a natural upper bound on their overlap with broken-string states, but introduces a new algorithm that successfully observes string-breaking signals.

Contribution

It establishes an upper bound on Wilson loop overlap with broken-string states and presents a novel algorithm that detects string-breaking in the 3-D Z_2 gauge Higgs model.

Findings

Wilson loop overlap with broken-string states is naturally limited

New algorithm reduces variance and detects string-breaking signals

Sharp string-breaking signals observed up to very small values of Wilson loops

Abstract

Numerical experiments on most gauge theories coupled with matter failed to observe string-breaking effects while measuring Wilson loops only. We show that, under rather mild assumptions, the overlap of the Wilson loop operator with the broken-string state obeys a natural upper bound implying that the signal of string-breaking is in general too weak to be detected by the conventional updating algorithms. In order to reduce the variance of the Wilson loops in 3-D Z_2 gauge Higgs model we use a new algorithm based on the L\"uscher-Weisz method combined with a non-local cluster algorithm which allows to follow the decay of rectangular Wilson loops up to values of the order of 10^{-24}. In this way a sharp signal of string breaking is found.