Kondo physics of the Anderson impurity model by Distributional Exact Diagonalization

TL;DR

This paper applies the Distributional Exact Diagonalization method to the Anderson impurity model to accurately capture Kondo physics, demonstrating its effectiveness and limitations compared to NRG benchmarks.

Contribution

The paper introduces and validates the DED scheme for modeling Kondo physics in the Anderson impurity model, emphasizing the importance of the particle number constraint.

Findings

DED produces excellent spectra within the Kondo regime.

The particle number constraint enforces Fermi liquid behavior.

Computational feasibility decreases for very strong correlations (U/Γ≫10).

Abstract

The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on the ensemble averaged self-energy, and thus is essential for the description of Kondo physics within DED. Using the Numerical Renormalization Group (NRG) method as a benchmark, we show that DED yields excellent spectra, both inside and outside the Kondo regime for a moderate number of bath sites. Only for very strong correlations ($U/\Gamma\gg10$) does the number of bath sites needed to achieve good quantitative agreement become too large to be computationally feasible.