The dynamics of fundamental particles can be described by quantum field theory. There exist different approaches to extract physical quantities out of such a theory. The one which we are using here is the lattice approach, where the theory is discretized on a space-time lattice. The lattice approach is a well established method to regularize a quantum field theory and perform computer simulations of the underlying theory from first principles. However, if one wants to perform simulations at finite particle number density, i.e., finite chemical potential, for many theories this leads to the so-called sign problem, which renders the straightforward application of the lattice approach impossible. There exists a variety of methods to solve or at least milden the sign problem and perform lattice simulations at finite density.We here study two different theories at finite density, the Z_3 Gauge-Higgs model and scalar quantum electrodynamics with two flavors. Also for these two theories, at finite chemical potential, we run into the sign problem. Here we use dual transformations to solve it: It is possible for the studied models to rewrite the original degrees of freedom in terms of an alternative set of degrees of freedom, which we refer to as dual variables. In the dual representation the sign problem is gone and we are able to perform simulations at arbitrary chemical potential. Note that in this case the transformation to dual variables is an exact solution of the sign problem. However, it is not yet clear if such transformations can be applied to any quantum field theory or if they are limited to a subset of theories.In the dual representation we perform simulations of the Z_3 model and scalar QED at finite chemical potential to explore the phase structure of these models. In addition, for scalar QED, we study the connection of the condensation thresholds to the low-lying mass spectrum of the theory, which are expected to be directly related to each other.