Coherent propagation and decay of quasi-particles

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We will develop a real-space / momentum, real-time / frequency Green's function method to describe the decay of quasi-particles in the dynamics of realistic materials as seen in local and non-local $n$-point correlation functions. The focus will be on the decay due to charge scattering for either low energy excitations (magnons) or high energy excitations (x-ray induced excitons and resonances). Project P7 directly contributes to thread 3 on dynamical properties of correlated models and materials in excited states.We will extend the methods in our program package Quanty to calculate the dynamics of x-ray excited core states, and low energy magnetic and orbital excitations to include a material specific self-energy describing the decay. We will focus on correlated metals relevant within QUAST such as, Ce3Bi4Pd3, CeRu4Sn6, Co3Sn2S2, CeBa7Au4Si40 and TaS2 experimentally investigated within P1, P3, and P6. We will use LDA+DMFT as a starting point for the electronic structure calculations. We will implement methods to calculate the change in the dynamics of x-ray core excited states as a result of the Auger-Meitner decay due to Coulomb scattering of local electrons into the continuum. In order to evade excessively large Hilbert spaces, we will implement the Coulomb scattering into non-local states as a self-energy for the electronic propagation of the quasi-particle. The propagating quasi-particle in the case of x-ray excitations is a core-hole - valence-electron exciton. Having a non-zero self-energy makes the description of the dynamics easier as the system forgets long-time behaviour. We can test our methods by comparing 2- and 4-point correlation functions to the x-ray absorption and resonant inelastic x-ray scattering of the model correlated metals measured (P1) and calculated (P1, P5) within QUAST. After we understand how to treat the self-energy of core excited states we will implement the self-energy of low energy magnetic excitations due to charge scattering. In the frequency domain this allows one to not only obtain an energy momentum dispersion of magnetic excitations in materials like Ce3Bi4Pd3, CeRu4Sn6, Co3Sn2S2 and CeBa7Au4Si40 but also their line widths. In the time domain the self-energy sets a time scale for the transfer of excitation energy between the spin and charge degrees of freedom of the material. Thereby setting time scales for the equilibration of the slow spin dynamics (P8).