Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation is resolved and Monte Carlo simulations at arbitrary chemical potential become possible. A suitable algorithm based on plaquette occupation numbers and link-fluxes is introduced and we analyze the model at zero temperature and finite density both in the weak and strong coupling phases. We show that at zero temperature the model has different first order phase transitions as a function of the chemical potential both for the weak and strong coupling phases. The exploratory study demonstrates that alternative degrees of freedom may successfully be used for Monte Carlo simulations in several systems with gauge and matter fields.