Real-frequency four-point correlation functions for probing inelastic and nonlocal effects in strongly correlated systems

• Applicant: Professor Dr. Jan von Delft, since 4/2022
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 403832751

In systems of interacting quantum particles, a particle can scatter inelastically by transferring its energy to another particle via interaction, and interactions mediate correlations between particles separated in space. The inelastic scattering and nonlocal correlations are theoretically described as four-point correlation functions and experimentally measurable in terms of dynamical properties as functions of real frequencies. However, the non-perturbative computation of real-frequency four-point functions had been intractable. Recently, within the framework of the preceding grant, we have achieved a breakthrough by developing a numerical renormalization group (NRG) method for computing local four-point functions for temperatures and frequencies---imaginary or real---of all magnitudes, from large to arbitrarily small ones. In the proposed project, I will apply the new method to study inelastic scattering in quantum impurity systems (superconducting circuits and quantum dots) and nonlocal correlations in strongly correlated lattice systems (Mott systems, Hund metals, and heavy-fermion materials). For the latter, we will consider effective impurity models given by dynamical mean-field theory (DMFT) solutions of lattice systems, and obtain the momentum dependence of four-point functions by using Feynman-diagrammatic treatments. The project will reveal how inelastic scattering and nonlocal correlations are reflected in experimentally observable quantities, such as transport properties, nonlocal dynamical susceptibilities, and resonant inelastic x-ray scattering (RIXS) spectra.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Seung-Sup Lee, Ph.D., until 4/2022