The sign problem and the simulation of quantum field theories at finite densities
The recent past has seen significant progress in solving the sign problem in dense matter quantum field theories.
As an example, I will discuss the physics of the 2+1 dimensional quantum O(2) model with a particular emphasis on the dense superfluid phase. Subsequently, the LLR algorithm will be introduced which allows to calculate the density of states with exponential error suppression. I will explain why this might be a generic solution of the sign problem for a wide class of theories.