Simulation strategies for the massless lattice Schwinger model in the dual formulation

TL;DR

This paper explores simulation strategies for the massless lattice Schwinger model in its dual form, enabling Monte Carlo studies by overcoming complex action issues through novel update algorithms involving plaquette-surfaces and fermion loops.

Contribution

It introduces a new combined update strategy using locally growing plaquette-surfaces and worm algorithms for fermion loops in the dual formulation.

Findings

The update strategy is validated against conventional simulations.

The approach successfully overcomes complex action problems.

Physical implications of the results are discussed.

Abstract

The dual form of the massless Schwinger model on the lattice overcomes the complex action problems from two sources: a topological term, as well as non-zero chemical potential, making these physically interesting cases accessible to Monte Carlo simulations. The partition function is represented as a sum over fermion loops, dimers and plaquette-surfaces such that all contributions are real and positive. However, these new variables constitute a highly constrained system and suitable update strategies have to be developed. In this exploratory study we present an approach based on locally growing plaquette-surfaces surrounded by fermion loop segments combined with a worm based strategy for updating chains of dimers, as well as winding fermion loops. The update strategy is checked with conventional simulations as well as reference data from exact summation on small volumes and we discuss some physical implications of the results.