A real-frequency solver for the Anderson impurity model based on bath optimization and cluster perturbation theory

TL;DR

This paper introduces a novel real-frequency solver for the Anderson impurity model that combines bath discretization, optimization via unitary transformations, and cluster perturbation theory to accurately compute Green's functions.

Contribution

The work presents a new approach that discretizes the bath directly on the real-frequency axis and optimizes it for improved impurity problem solutions.

Findings

Enables direct real-frequency bath discretization with ~50 sites.

Separates the bath into weakly coupled parts for efficient computation.

Calculates Green's functions using a combination of ED and cluster perturbation theory.

Abstract

Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites ($\approx 50$). Then, the bath is optimized by unitary transformations such that it separates into two parts that are weakly coupled. One part contains the impurity site and its interacting Green's functions can be determined with ED. The other (larger) part is a non-interacting system containing all the remaining bath sites. Finally, the Green's function of the full AIM is calculated via coupling these two parts with cluster perturbation theory.