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arXiv 0910.1206hep-lat
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QCD符号问题的随机矩阵分析

Random matrix analysis of the QCD sign problem

Jacques Bloch, Tilo Wettig

摘要:

用费米子行列式的平均相位度量了非零重子密度下格点量子色动力学中符号问题的严重性。受手征随机矩阵理论和QCD在夸克体系中与首序等价的启发,我们计算了随机矩阵理论中一般拓扑的费米子行列式的相位随夸克化学势和夸克质量的变化.我们发现符号问题随着拓扑荷的增加而变得更加温和。详细的数值随机矩阵模拟的分析预测进行了验证。

英文摘要:

The severity of the sign problem in lattice QCD at nonzero baryon density is measured by the average phase of the fermion determinant. Motivated by the equivalence of chiral random matrix theory and QCD to leading order in the epsilon regime, we compute the phase of the fermion determinant for general topology in random matrix theory as a function of the quark chemical potential and the quark mass. We find that the sign problem becomes milder with increasing topological charge. The analytic predictions are verified by detailed numerical random matrix simulations.

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