Full density matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

TL;DR

This paper evaluates the full density matrix approach within numerical renormalization group methods for calculating thermodynamic properties of the Anderson impurity model, comparing results with traditional NRG and Bethe ansatz benchmarks.

Contribution

It demonstrates the effectiveness of the FDM approach for thermodynamic calculations and discusses subtle aspects in susceptibility computations within this framework.

Findings

FDM yields accurate susceptibility and specific heat results compared to Bethe ansatz.

Susceptibilities to local and uniform fields coincide in the wide-band limit.

Identifies a subtlety in susceptibility calculation within FDM.

Abstract

Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.