Abstract:
We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that large complex bags with positive and negative weights come with equal probabilities. On the other hand simple bags have a large probability of having a positive weight. In analogy with the meron cluster approach, we suggest that eliminating the complex bags from the partition function should alleviate the sign problem while capturing the important physics. We also find a modified model containing only simple bags which does not suffer from any sign problem and argue that it contains a parity breaking phase transition similar to the original model. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative.
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