具有轮廓变形的手征随机矩阵模型的符号问题
Fighting the sign problem in a chiral random matrix model with contour deformations
摘要：
我们研究了Stephanov手征随机矩阵理论中的积分轮廓变形，目的是减轻有限密度符号问题。对变形的积分轮廓线进行了简单的处理，并对其参数进行了优化。我们发现，一个单一的参数的优化管理显着改善的严重性的迹象问题。我们展示了数值证据，表明所实现的改进在系统的自由度上是指数级的，即，随机矩阵的大小。我们还比较了优化方法与来自全纯流方程的轮廓变形。
英文摘要：
We studied integration contour deformations in the chiral random matrix theory of Stephanov with the goal of alleviating the finite-density sign problem. We considered simple ansätze for the deformed integration contours, and optimized their parameters. We find that optimization of a single parameter manages to considerably improve on the severity of the sign problem. We show numerical evidence that the improvement achieved is exponential in the degrees of freedom of the system, i.e., the size of the random matrix. We also compare the optimization method with contour deformations coming from the holomorphic flow equations.
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