论文标题
从弱耦合到单位性的四阶病毒系数
The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
论文作者
论文摘要
在当前的精确量子多体物理学时代，最严格的系统之一是非层次主义旋转$ 1/2 $费米气体的单一限制，因为它的简单性和与原子，凝结物质和核物理学相关性。这种密切相关的系统的热力学由通用功能确定，在高温下，该功能受通用病毒系数$ b_n $控制，$ b_n $捕获了$ n $ body System对多体动力学的影响。目前，$ b_2 $和$ b_3 $的理解众所周知，但是对于$ b_4 $而言，情况尚不清楚，也没有对$ b_5 $做出预测。为了回答这些开放的问题，我们使用逐步使用更精细的时间晶格间距，基于假想时间演化运算符的Trotter-Suzuki分解来实现一种非扰动分析方法。实施这些因素化和自动化代数代码，我们获得了相互作用诱导的变化$ΔB_n$从弱耦合到单位性。在Unitarity上，我们发现：$ΔB_3= -0.356（4）$，与先前的结果一致； $ΔB_4= 0.062（2）$，与所有以前的理论估计相一致，但与实验确定不一致； $ΔB_5= 0.078（6）$，这是一个预测。我们展示了这些答案对状态和棕褐色接触密度方程的影响，并将其起源跟踪回它们的偏振和非极化组件。
In the current era of precision quantum many-body physics, one of the most scrutinized systems is the unitary limit of the nonrelativistic spin-$1/2$ Fermi gas, due to its simplicity and relevance for atomic, condensed matter, and nuclear physics. The thermodynamics of this strongly correlated system is determined by universal functions which, at high temperature, are governed by universal virial coefficients $b_n$ that capture the effects of the $n$-body system on the many-body dynamics. Currently, $b_2$ and $b_3$ are well understood, but the situation is less clear for $b_4$, and no predictions have been made for $b_5$. To answer these open questions, we implement a nonperturbative analytic approach based on the Trotter-Suzuki factorization of the imaginary-time evolution operator, using progressively finer temporal lattice spacings. Implementing these factorizations and automated algebra codes, we obtain the interaction-induced change $Δb_n$ from weak coupling to unitarity. At unitarity, we find: $Δb_3 = -0.356(4)$, in agreement with previous results; $Δb_4 = 0.062(2)$, in agreement with all previous theoretical estimates but at odds with experimental determinations; and $Δb_5 = 0.078(6)$, which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and track their origin back to their polarized and unpolarized components.
