Dynamical mean-field theory describes the impact of strong local correlation effects in many-electron systems. While the single-particle spectral function is directly obtained within the formalism, two-particle susceptibilities can also be obtained by solving the Bethe-Salpeter equation. The solution requires handling infinite matrices in Matsubara frequency space. This is commonly treated using a finite frequency cutoff, resulting in slow linear convergence. A decomposition of the two-particle response in local and nonlocal contributions enables a reformulation of the Bethe-Salpeter equation inspired by the dual boson formalism. The reformulation has a drastically improved cubic convergence with respect to the frequency cutoff, considerably facilitating the calculation of susceptibilities in multi-orbital systems. This improved convergence arises from the fact that local contributions can be measured in the impurity solver. The dual Bethe-Salpeter equation uses the fully reducible vertex which is free from vertex divergences. We benchmark the approach on several systems including the spin susceptibility of strontium ruthenate ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, a strongly correlated Hund's metal with three active orbitals.

中文翻译：

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动态平均场理论中多轨道晶格磁化率的对偶 Bethe-Salpeter 方程

动态平均场理论描述了多电子系统中强局部相关效应的影响。虽然单粒子谱函数是在形式主义中直接获得的，但双粒子磁化率也可以通过求解 Bethe-Salpeter 方程来获得。该解决方案需要处理松原频率空间中的无限矩阵。通常使用有限频率截止来处理此问题，导致线性收敛缓慢。局部和非局部贡献中双粒子响应的分解使得受双玻色子形式主义启发的 Bethe-Salpeter 方程得以重新表述。重新公式在截止频率方面显着提高了三次收敛性，极大地促进了多轨道系统中磁化率的计算。这种改进的收敛性源于可以在杂质求解器中测量局部贡献这一事实。对偶 Bethe-Salpeter 方程使用完全可约顶点，没有顶点散度。我们在多个系统上对该方法进行了基准测试，包括钌酸锶的自旋敏感性${锶}_2{\mathrm{氧化钌}}_4$，一种具有三个活性轨道的强相关洪德金属。