Overcoming the sign problem in one-dimensional QCD by new integration rules with polynomial exactness
2016
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 $N\le 3$. The method is applied to the example of 1-dimensional QCD with a
chemical potential. We explore, in particular, regions of the
parameter spacein which the sign problem appears due the presence of the
chemical potential. While
Markov Chain Monte Carlofails 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 our new method leads to orders of magnitude reduced errors also in other regions of
parameter space.
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