部分玻色化集体涨落对电子自由度的影响
Impact of partially bosonized collective fluctuations on electronic degrees of freedom
摘要：
本文全面分析了集体电子涨落及其对哈伯德模型单粒子性质的影响。我们的方法是基于一个标准的双费米子/玻色子计划截断在两粒子水平的相互作用。在这个框架内，我们比较不同的一组图（阶梯与精确的图解蒙特卡罗），和/或在四点相互作用顶点的形式（精确与部分玻色化）的各种近似。这允许评估四点顶点函数的所有分量对电子自能的影响。特别是，我们观察到的贡献，不占部分玻色子近似的顶点只有一个很小的影响，在广泛的模型参数范围内的电子自由度。此外，我们发现，在该制度，在阶梯对偶费米子近似提供了一个准确的解决方案的问题，主导的贡献，自能是由双曲玻色子模式。这可以解释的事实，横向粒子-空穴和粒子-粒子模式的贡献部分相互抵消。我们的研究结果证明了最近推出的双三重不可约的本地扩展（D-TRILEX）的方法，代表一个最简单的一致的图形扩展的动态平均场论的适用性。我们发现，自洽的D-TRILEX方法是相当准确的，也在具有挑战性的制度的哈伯德模型，即使在动态平均场论不提供最佳的局部参考点（杂质问题）的图形扩展。
英文摘要：
In this work we present a comprehensive analysis of collective electronic fluctuations and their effect on single-particle properties of the Hubbard model. Our approach is based on a standard dual fermion/boson scheme with the interaction truncated at the two-particle level. Within this framework we compare various approximations that differ in the set of diagrams (ladder vs exact diagrammatic Monte Carlo), and/or in the form of the four-point interaction vertex (exact vs partially bosonized). This allows to evaluate the effect of all components of the four-point vertex function on the electronic self-energy. In particular, we observe that contributions that are not accounted for by the partially bosonized approximation for the vertex have only a minor effect on electronic degrees of freedom in a broad range of model parameters. In addition, we find that in the regime, where the ladder dual fermion approximation provides an accurate solution of the problem, the leading contribution to the self-energy is given by the longitudional bosonic modes. This can be explained by the fact that contributions of transverse particle-hole and particle-particle modes partially cancel each other. Our results justify the applicability of the recently introduced dual triply irreducible local expansion (D-TRILEX) method that represents one of the simplest consistent diagrammatic extensions of the dynamical mean-field theory. We find that the self-consistent D-TRILEX approach is reasonably accurate also in challenging regimes of the Hubbard model, even where the dynamical mean-field theory does not provide the optimal local reference point (impurity problem) for the diagrammatic expansion.
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