Adaptive cluster approximation for reduced density-matrix functional theory

2016/12/31 by Robert R. Schade, Robert Schade, Peter E. Blöchl · 9 citations
Chemistry · Mathematics · Physics and Astronomy · #Anderson impurity model #Chemistry #Cluster (spacecraft) #Computer science #Density functional theory #Density matrix #Formalism (music) #Impurity #Mathematics #Matrix (chemical analysis) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #Theoretical and Computational Physics #Unitary state #Unitary transformation #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.97.245131

published in Physical review. B./Physical review. B 97(24) (American Physical Society) · 15 pages, 8 figures

arxiv created 2018/05/16 · openalex publication_date 2018/06/20 · arxiv updated 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A method, called the adaptive cluster approximation (ACA), for single-impurity Anderson models is proposed. It is based on the 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 exactly 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.

Citations

• Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v -representability problem
• Density-matrix functional theory of the Hubbard model: An exact numerical study
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• Conditioning of quasi-Newton methods for function minimization
• Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction
• Density-matrix algorithms for quantum renormalization groups
• A family of variable-metric methods derived by variational means
• Multiplier and gradient methods
• Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models
• Matrix product states represent ground states faithfully
• Testing one-body density functionals on a solvable model
• A new approach to variable metric algorithms
• The density-matrix renormalization group in the age of matrix product states
• Resistance Minimum in Dilute Magnetic Alloys
• Self-Consistent Equations Including Exchange and Correlation Effects