通过新的积分规则克服一维QCD中的符号问题
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
AI总结：
本文提出一种新的积分方法，用于U(N)和SU(N)群，验证其对N≤3的多项式精确性，并应用于具有化学势的一维QCD，克服符号问题并减少误差。
摘要：
在本文中，我们描述了一种新的积分方法，用于U(N)和SU(N)群，我们验证了该方法在N≤3时的多项式精确性。该方法应用于具有化学势的一维QCD的例子。我们特别探讨了由于化学势存在而导致符号问题出现的参数空间区域。尽管马尔可夫链蒙特卡洛方法在此区域失效，我们的新积分方法仍能以任意精度计算宇称凝聚子，清楚地表明其克服了符号问题。此外，我们还展示了该方法在参数空间的其他区域也导致误差减少一个数量级。
英文摘要：
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 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 our new method leads to orders of magnitude reduced errors also in other regions of parameter space.
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