Adaptive cluster approximation for reduced density-matrix functional theory

TL;DR

The paper introduces the adaptive cluster approximation (ACA), a new method for efficiently modeling single-impurity Anderson systems using reduced density-matrix functional theory, focusing computational effort on a small, relevant cluster.

Contribution

It proposes the ACA method that transforms bath states to focus on a small cluster, enabling accurate and efficient calculations for impurity models.

Findings

Rapid convergence to exact results with increasing cluster size

Effective reduction of bath complexity in impurity models

Potential for accurate simulations with smaller computational resources

Abstract

A method, called the adaptive cluster approximation (ACA), for single-impurity Anderson models is proposed. It is based on reduced density-matrix functional theory, where the one-particle reduced density matrix is used as the basic variable. The adaptive cluster approximation introduces a unitary transformation of the bath states such that the effect of the bath is concentrated to a small cluster around the impurity. For this small effective system one can then either calculate the reduced density-matrix functional numerically exact from Levy's constrained-search formalism or approximate it by an implicit approximation of the reduced density-matrix functional. The method is evaluated for single-impurity Anderson models with finite baths. The method converges rapidly to the exact result with the size of the effective bath.