Dual Lattice Simulation of the Abelian Gauge-Higgs Model at Finite Density: An Exploratory Proof of Concept Study

The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical potential is mapped exactly to a dual representation where matter fields correspond to loops of flux and the gauge fields are represented by surfaces. The complex action problem of the conventional formulation at finite chemical potential μ is overcome in the dual representation, and the partition sum has only real and nonzero contributions. We simulate the model in the dual representation using a generalized worm algorithm, explore the phase diagram, and study condensation phenomena at finite μ.