Dynamical vertex functions of many-electron systems

更广泛的研究背景-我们的项目旨在在多电子问题的量子场论描述方面取得实质性进展。我们专注于最具挑战性的理论方面之一：相关量子材料中两粒子散射过程的物理。在费曼图的领域中，这些过程用顶点函数来描述，即在两粒子水平上对自能的模拟。独创性/创新水平-掌握顶点函数，类似于目前可能的自我能量，代表了相互作用费米子的多体理论和对潜在物理的完整理解的关键一步。此外，它将显著提高量子材料的光谱和输运性质的实际计算的预测能力。研究问题/目标-我们计划的第一个目标是研究不可约顶点函数的发散对物理和算法的影响，最近发现这些发散发生在相关电子的基本模型中。这些异常与Luttinger-Ward泛函的潜在多值性有关，在几个基本方面挑战了当前的理论理解。我们计划对不断增加的物理复杂性进行彻底的研究，旨在揭示这些分歧所起的真正作用，迄今为止，这些分歧仅在形式上被理解。我们的第二个目标是处理物理响应函数中两粒子相关性的影响：顶点修正。由于它们的数值复杂性，它们经常被忽略或严重近似。我们将填补当前文献的相关空白，通过计算出顶点修正不再是对称禁止的一般条件，并且必须在模型和材料计算中考虑。然后，我们将分析由顶点修正引起的大部分未开发的现象学，以动态敏感性和电导率，在最先进的多体方法中计算它们，用于特殊物理兴趣的情况。在项目的最后阶段，我们将顶点形式化扩展到对称性降低的系统，包括自旋轨道耦合效应和远程有序相。这将允许磁性和拓扑材料的完整“理论光谱”，到目前为止仅在弱耦合近似范围内进行研究。方法-我们计划的研究将依赖于先进的多体方法，如多轨道动力学平均场理论及其扩展，并在需要时使用半解析或图解计算。参与的主要研究人员-该项目雄心勃勃的科学议程将通过参与的两位pi （Alessandro Toschi和Giorgio Sangiovanni）的联合专业知识成为可能，他们的团队之间的长期合作极大地受益。

Wider research context - Our project aims at a substantial advancement in the quantum field theory description of the many-electron problem. We focus on one of the most challenging theoretical aspects: the physics of two-particle scattering processes in correlated quantum materials. In the realm of the Feynman diagrammatic these processes are described by the vertex-functions, i.e. the analog of the self-energy on the two-particle level.Level of originality/innovation - Mastering the vertex functions, similarly as it is presently possible for the self- energy, represents a pivotal step for the many-body theory of interacting fermions and for a complete understanding of the underlying physics. Further, it will significantly raise the predictive power of realistic calculations of spectroscopic and transport properties of quantum materials.Research questions/objectives - The first objective of our program is the investigation of the physical and algorithmic impact of the divergences of the irreducible vertex functions, recently discovered to occur in basic models of correlated electrons. These anomalies, associated to an underlying multivaluedness of the Luttinger-Ward functionals, challenge the current theoretical understanding in several fundamental aspects. We plan thorough studies of increasing physical complexity, designed to unveil the true role played by these divergences, hitherto understood only at a mere formal level.Our second goal deals with the effects of two-particle correlations in physical response functions: the vertex corrections. Due to their numerical complexity, these are often neglected or severely approximated. We will fill a relevant gap of the current literature, by working out the general conditions under which vertex corrections are no longer symmetry-forbidden and have to be taken into account in model and material calculations. Then, we will analyze the largely unexplored phenomenology induced by vertex corrections to dynamical susceptibilities and conductivities, calculating them within state-of-the-art many-body methods for cases of special physical interest.In the final stage of the project, we will extend the vertex formalism to systems with reduced symmetry, including also spin-orbit coupling effects and long-range ordered phases. This will allow for a full “theoretical spectroscopy” of magnetic as well as topological materials, investigated so far within weak-coupling approximations only.Methods - Our planned research will rely on advanced many-body approaches such as multi-orbital dynamical mean-field theory and its extensions and, where needed, on semi-analytic or diagrammatic calculations.Primary researcher involved - The ambitious scientific agenda of this project will be made possible by the joint expertise of the two PIs involved (Alessandro Toschi and Giorgio Sangiovanni), greatly profiting from the long-standing cooperation between their groups.