Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions
Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions
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克服非相对论计算中的符号问题：质量不平衡费米子的案例研究
DOI：
10.1103/physrevd.96.094506
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发表时间：
2017
影响因子：
5
通讯作者：
J. Braun
中科院分区：
文献类型：
--
作者：
L. Rammelmüller;W. J. Porter;J. E. Drut;J. Braun
质量不平衡费米系统的基态和热力学计算是一个具有挑战性的多体问题。即使在一个空间维度上，解析解也仅限于特殊的配置，并且标准蒙特卡罗方法的数值进展受到符号问题的阻碍。目前工作的重点是进一步发展的方法来研究不平衡系统在一个完全非微扰的方式。我们报告我们的计算质量不平衡费米子的基态能量使用两种不同的方法，这也是非常流行的强相互作用理论（量子色动力学，QCD）的背景下：（a）混合Monte Carlo算法与虚质量不平衡，其次是解析延续到真实的轴;和（B）复杂的朗之万算法。我们涵盖了一系列的现场相互作用强度，包括强吸引力以及强排斥的情况下，我们验证与非微扰重整化群方法和微扰理论。我们的研究结果表明，对于强排斥耦合，能量开始变平，这意味着有趣的结果，为短程和高频相关函数。总的来说，我们的结果清楚地表明，复杂的朗之万方法是非常通用的，非常适合不平衡的费米气体的吸引力和排斥力的相互作用。
The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with standard Monte Carlo approaches is hindered by the sign problem. The focus of the present work is on the further development of methods to study imbalanced systems in a fully nonperturbative fashion. We report our calculations of the ground-state energy of mass-imbalanced fermions using two different approaches which are also very popular in the context of the theory of the strong interaction (quantum chromodynamics, QCD): (a) the hybrid Monte Carlo algorithm with imaginary mass imbalance, followed by an analytic continuation to the real axis; and (b) the complex Langevin algorithm. We cover a range of on-site interaction strengths that includes strongly attractive as well as strongly repulsive cases which we verify with nonperturbative renormalization group methods and perturbation theory. Our findings indicate that, for strong repulsive couplings, the energy starts to flatten out, implying interesting consequences for short-range and high-frequency correlation functions. Overall, our results clearly indicate that the complex Langevin approach is very versatile and works very well for imbalanced Fermi gases with both attractive and repulsive interactions.