论文标题
示意图扩展的算法方法，用于对易感函数的实际评估
Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
论文作者
论文摘要
我们系统地生成了Feynman Mingrammatic形式主义的两粒子自旋敏感性的扰动膨胀，并将这种扩展应用于模型系统 - 平方晶格上的单频段哈伯德模型。我们利用算法Matsubara Integration（AMI）[A. Taheridehkordi，S。H。Curnoe和J. P. F. Leblanc，物理。 Rev. b 99，035120（2019）]分析评估Matsubara频率求和，使我们能够象征性地将分析延续到真实频率轴上。我们通过应用图形不变转换来最大程度地减少计算费用[Amir Taheridehkordi，S。H. Curnoe和J. P. F. Leblanc，Phys。 Rev. B 101，125109（2020）]。我们重点介绍了随机相近似和T矩阵方法的扩展，这些方法由于AMI而变得可拖延。我们提出了弱相互作用强度的结果，其中直接扰动膨胀是收敛的，并通过与其他数值方法相比，在Matsubara轴上验证了我们的结果。通过通过逐阶扩展来检查自旋敏感性是实际频率的函数，我们可以精确地确定高阶校正在旋转易感性上的作用，并证明了我们方法的实用性和局限性。
We systematically generate the perturbative expansion for the two-particle spin susceptibility in the Feynman diagrammatic formalism and apply this expansion to a model system - the single-band Hubbard model on a square lattice. We make use of algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] to analytically evaluate Matsubara frequency summations, allowing us to symbolically impose analytic continuation to the real frequency axis. We minimize our computational expense by applying graph invariant transformations [Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 101, 125109 (2020)]. We highlight extensions of the random-phase approximation and T-matrix methods that, due to AMI, become tractable. We present results for weak interaction strength where the direct perturbative expansion is convergent, and verify our results on the Matsubara axis by comparison to other numerical methods. By examining the spin susceptibility as a function of real-frequency via an order-by-order expansion we can identify precisely what role higher order corrections play on spin susceptibility and demonstrate the utility and limitations of our approach.
