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的实质性进展。我们专注于最具挑战性的理论方面之一：相关量子材料中的两粒子散射过程的物理学。在费曼图解的领域中，这些过程由顶点函数来描述，即在两粒子水平上的自能的模拟。独创性/创新水平-掌握顶点函数，就像目前掌握自能一样，代表了相互作用费米子的多体理论和对基础物理的完整理解的关键一步。此外，它将显着提高量子材料的光谱和输运性质的现实计算的预测能力。研究问题/目标-我们计划的第一个目标是调查的物理和算法的影响的分歧的不可约顶点功能，最近发现发生在相关电子的基本模型。这些异常，与一个潜在的多值的Luttinger-Ward泛函，挑战目前的理论理解在几个基本方面。我们计划深入研究日益增加的物理复杂性，旨在揭示这些分歧所发挥的真正作用，迄今为止，只在仅仅是形式上的水平理解。我们的第二个目标涉及物理响应函数中的两粒子相关性的影响：顶点校正。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被禁止的一般条件，并在模型和材料计算中考虑到。然后，我们将分析由顶点修正引起的动力学极化率和电导率的大量未探索的现象学，在最先进的多体方法中计算它们，用于特殊物理感兴趣的情况。在项目的最后阶段，我们将把顶点形式主义扩展到具有约化对称性的系统，包括自旋轨道耦合效应和长程有序相。这将允许一个完整的“理论光谱”的磁性以及拓扑材料，调查到目前为止，在弱耦合approximations.Methods -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，半解析或图解计算。主要研究人员参与-该项目雄心勃勃的科学议程将通过参与的两名PI（Alessandro Toschi和Giorgio Sangiovanni）的联合专业知识成为可能，并从他们之间的长期合作中受益匪浅。

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.