Overcoming the sign problem in one-dimensional QCD by new integration rules with polynomial exactness

In this paper we describe a new integration method for the groups U(N) and SU(N), for which we verified numerically that it is polynomially exact for N <= 3. The method is applied to the example of one-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that also in other regions of parameter space our new method leads to errors which are reduced by orders of magnitude.