arXiv 2201.047982022-01-13cond-mat.quant-gas

强相互作用费米气体II的超高斯对涨落理论：对称性破缺相

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases II: The broken-symmetry phase

Brendan C. Mulkerin, Xing-Can Yao, Yoji Ohashi, Xia-Ji Liu, Hui Hu

备注：: 13 pages, 6 figures

摘要：

本文应用最近提出的强耦合理论，在高斯水平上研究了从Bardeen-Cooper-Schrieffer（BCS）超流体到玻色-爱因斯坦凝聚体（BEC）交叉处强相互作用费米气体的热力学性质.超高斯对涨落理论（GPF）总是遵循严格的热力学关系，在BEC极限下恢复了Bogoliubov分子理论，并具有接近正确的分子-分子散射长度。我们表明，超越GPF理论在BEC-BCS交叉处定量准确地预测了基态性质，与Horikoshi \textit{et al.}最近在Phys. Rev. X \textbf{7}，041004（2017）中的测量结果非常一致。在具有无限大的$s$ -波散射长度的幺正极限中，超越GPF理论预测了一个可靠的普适能量状态方程，其值可达0.6 $T_c$，其中$T_c$是幺正态下的超流转变温度。该理论预测了零温下的Bertsch参数$ξ\simeq 0.365$，与最新的量子蒙特卡罗结果$ξ= 0.367(7)$和最新的实验测量值$ξ= 0.367(9)$吻合得很好.我们归因于良好的和广泛的适用性的超GPF理论在破缺对称性阶段的合理的重新求和费曼图以下的一个维度$ε$ -展开分析近四维（$d=4-ε$），这引起了准确的预测在二阶$\mathcal{O}(ε^2)$。我们的工作表明，进一步改进强相互作用费米子的强耦合理论的基础上，在更高的阶$\mathcal{O}(ε^n)$与$n\ge 3$系统包含的大回路费曼图的可能性。

英文摘要：

We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body $T$-matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi \textit{et al.} in Phys. Rev. X \textbf{7}, 041004 (2017). In the unitary limit with infinitely large $s$-wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6$T_c$, where $T_c$ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter $ξ\simeq 0.365$ at zero temperature, in good agreement with the latest quantum Monte Carlo result $ξ= 0.367(7)$ and the latest experimental measurement $ξ= 0.367(9)$. We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase to the reasonable re-summation of Feynman diagrams following a dimensional $ε$-expansion analysis near four dimensions ($d=4-ε$), which gives rise to accurate predictions at the second order $\mathcal{O}(ε^2)$. Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders $\mathcal{O}(ε^n)$ with $n\ge 3$.

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