Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
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DOI：
10.1103/physrevd.91.101701
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发表时间：
2015-04
影响因子：
5
通讯作者：
Y. Tanizaki;Hiromichi Nishimura;K. Kashiwa
中科院分区：
文献类型：
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作者：
Y. Tanizaki;Hiromichi Nishimura;K. Kashiwa
考虑了平均场近似中出现的费米子符号问题，采用lefschetz -顶针法设计了自由能的系统计算方案。我们证明了lefschetz -顶针法尊重反射对称性，这使得物理量在使用复鞍点的任何阶近似下都明显实数。以Airy积分为例对公式进行了论证，并详细讨论了该公式在稠密QCD的polyakov环有效模型中的应用。
The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.