具有虚质量不平衡的费米气体与Monte Carlo计算中的符号问题
Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations
摘要：
费米气体在强耦合状态下，如幺正极限，对多体方法来说是具有挑战性的。虽然已经取得了很大的进展与纯分析方法，定量结果需要从头算数值方法，如蒙特卡罗（MC）计算。然而，质量不平衡和自旋不平衡的气体，由于臭名昭著的符号问题，无法进入MC计算。最近有人指出，符号问题，有限自旋不平衡，可以绕过诉诸虚极化和解析延拓。由温度和极化跨越的相图的大部分然后变得可用于MC计算。我们建议将类似的策略应用到质量不平衡的情况下，这开辟了可能性，研究与MC计算相关联的相图。特别是，我们的分析表明，在这个相图中的（三）临界点的检测是可能的。我们还讨论了计算中的零温度限制与我们的方法。
英文摘要：
Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical approaches, such as Monte Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. It was recently pointed out that the sign problem, for finite spin imbalance, can be circumvented by resorting to imaginary polarizations and analytic continuation. Large parts of the phase diagram spanned by temperature and polarization then become accessible to MC calculations. We propose to apply a similar strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. In particular, our analysis suggests that a detection of a (tri-)critical point in this phase diagram is possible. We also discuss calculations in the zero-temperature limit with our approach.
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