Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Daniel Göschl,M Della Morte,E Gámiz Sánchez,C Pena Ruano,P Fritzsch

doi:10.1051/epjconf/201817507002

Abstract

We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

Highlights

In recent years dual representations have been successfully used to overcome complex action problems for a variety of lattice field theories
In this presentation we explore the dual formulation of the massless lattice Schwinger model for its use in Monte Carlo simulations
The dual representation has only real and positive weights and the complex action problem is solved, we have to deal with highly constrained systems of fermion loops and dimers

Summary

Introduction

In recent years dual representations have been successfully used to overcome complex action problems for a variety of lattice field theories (see, e.g., the reviews [1,2,3,4,5]). The crucial difference of the two fermion actions is that we use the complex conjugate link variables Uν(n)∗ = Uν(n)−1 for the second flavor χ, implying opposite charges for ψ and χ. This implements Gauss’ law, which requires overall electric neutrality. The sum runs over all admissible configurations of the loop (l, l) and dimer (d, d) occupation numbers of both flavors and the plaquette occupation number p. For faster propagation through phase space we use global gauge/plaquette updates for both cases and local updates for electrically neutral loops in the two-flavor case

Local updates

Worm update for the dimers

Updates for winding neutral double loops

Results for the one-flavor model

Results for the two-flavor model

Conclusion