T-Matrix Formulation of Impurity Scattering in Correlated Systems

TL;DR

This paper develops a generalized T-matrix approach to include Coulomb correlations in impurity scattering, providing a framework to analyze resonant and bound states in correlated electron systems.

Contribution

It introduces a dynamic, symmetry-aware T-matrix formulation that accurately captures impurity effects in strongly correlated models like the t-J and Hubbard models.

Findings

Reproduces exact resonant and bound impurity states

Provides a static approximation for effective impurity potentials

Demonstrates the importance of Coulomb correlations in scattering processes

Abstract

Using a generalized T-matrix description which, in principle, exactly includes Coulomb correlations and potential scattering events, resonant and bound impurity states are discussed. Like in the non-interacting case, the effects of the scattering potential can be divided into different partial wave channels, exploiting the symmetry of the underlying lattice. Due to Coulomb correlations bare local (i.e.\ s-wave) potentials become dynamic and extended, being responsible also for p-, d-wave etc. scattering effects. Numerically exact results for both the two-dimensional t--J and Hubbard models are used to construct a simple (static) approximation to the effective impurity potential which is shown to reproduce the exact resonant scattering and bound states in the relevant symmetry channels.