Capturing nonlocal correlations in electronic systems — wo-particle response and parquet equations

Susceptibilities and optical conductivity are examples of two-particle response functions that are the key quantities for connecting theoretical predictions for correlated materials with experimental results. It can however become highly non-trivial to calculate them, especially in cases when nonlocal electronic correlations are important. In my talk I will explain what two-particle correlations are and when they become important. I will then present an overview of methods of their computation with the focus on diagrammatic methods. I will show results for two-particle (vertex) corrections to optical conductivity [1], that are present in systems with antiferromagnetic or charge density wave fluctuations, leading to a displaced Drude peak in correlated metals [2]. At the end I will discuss computational challenges and new methodological developments in the efficient representation of two-particle correlation functions with the use of quantics tensor trains [3,4]. [1] A. Kauch, P. Pudleiner, K. Astleithner, P. Thunström, T. Ribic, and K. Held, Phys. Rev. Lett. 124, 047401 (2020) [2] J. Krsnik, O. Simard, P. Werner, A. Kauch, and K. Held, Phys. Rev. B 110, 075118 (2024) [3] H. Shinaoka, M. Wallerberger, Y. Murakami, K. Nogaki, R. Sakurai, P. Werner, and A. Kauch, Phys. Rev. X 13, 021015 (2023) [4] S. Rohshap, M. Ritter, H. Shinaoka, J. von Delft, M. Wallerberger, and A. Kauch, Phys. Rev. Res. 7, 023087 (2025)‍