Quantum cluster theories

2004/04/02 by Th. Maier, Thomas Maier, M. Jarrell +5 · 39 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Cluster (spacecraft) #Computer science #Lattice (music) #Mathematics #Mean field theory #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum field theory #Quantum mechanics #Rotation formalisms in three dimensions #Statistical physics #Theoretical physics #cond-mat.str-el

paper · pdf · doi:10.1103/revmodphys.77.1027

submitted to Reviews of Modern Physics

arxiv created 2004/04/02 · openalex publication_date 2005/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

This article reviews quantum cluster theories, a set of approximations for infinite lattice models which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding mean-field approximation when the cluster size becomes 1. Although quantum cluster theories were originally developed to treat disordered systems, they have more recently been applied to the study of ordered and disordered correlated systems, which will be the focus of this review. After a brief historical review, the authors provide detailed derivations of three cluster formalisms: the cluster perturbation theory, the dynamical cluster approximation, and the cellular dynamical mean-field theory. They compare their advantages and review their applications to common models of correlated electron systems.

Citations

• Nonperturbative approach to full Mott behavior
• Lectures on Phase Transitions and the Renormalization Group
• Dynamical cluster approximation employing the fluctuation exchange approximation as a cluster solver
• Exact dynamical mean-field theory of the Falicov-Kimball model
• Correlation induced insulator to metal transitions
• Fluctuation-exchange supplemented quantum Monte Carlo approach to the Hubbard model
• Low-temperature Lanczos method for strongly correlated systems
• Hubbard model at infinite dimensions: Thermodynamic and transport properties
• Quantum Monte Carlo algorithm for nonlocal corrections to the dynamical mean-field approximation
• Fictive impurity models: An alternative formulation of the cluster dynamical mean-field method
• Cluster dynamical mean-field theories: Causality and classical limit
• A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
• A Reformulation of the Coherent Potential Approximation and Its Applications
• Systematic and causal corrections to the coherent potential approximation
• Numerical renormalization group calculations for the self-energy of the impurity Anderson model
• Theory of Superconductivity
• Review of techniques in the large-Nexpansion for dilute magnetic alloys
• Spectral Weight of the Hubbard Model through Cluster Perturbation Theory
• The renormalization group: Critical phenomena and the Kondo problem
• Many-body theory versus simulations for the pseudogap in the Hubbard model
• The critical properties of the two-dimensional xy model
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Spectral functions in itinerant electron systems with geometrical frustration
• Stripes in Doped Antiferromagnets: Single-Particle Spectral Weight
• Evolution of the stripe phase as a function of doping from a theoretical analysis of angle-resolved photoemission data
• Ordering, metastability and phase transitions in two-dimensional systems
• Self-energy-functional approach to systems of correlated electrons
• Magnetic and dynamic properties of the Hubbard model in infinite dimensions
• The pseudogap in high-temperature superconductors: an experimental survey
• Electron correlations in narrow energy bands
• Nonlocal Coulomb Interactions and Metal-Insulator Transition inTi2O3: A ClusterLDA+DMFTApproach
• Cluster methods for strongly correlated electron systems

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• Rashba Spin-Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems
• Improved estimators for the self-energy and vertex function in hybridization-expansion continuous-time quantum Monte Carlo simulations
• Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems
• Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems
• Microscopic theory of high-temperature superconductivity in strongly correlated electronic systems
• Gutzwiller description of non-magnetic Mott insulators: Dimer lattice model
• Anisotropic two‐orbital Hubbard model: Single‐site versus cluster Dynamical Mean‐Field Theory
• Electrodynamics of correlated electron materials
• Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory
• Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator
• Direct connection between Mott insulators and d-wave high-temperature superconductors revealed by continuous evolution of self-energy poles
• Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Cluster dynamical mean field theory of quantum phases on a honeycomb lattice
• Validity of the spin-susceptibility “glue” approximation for pairing in the two-dimensional Hubbard model
• Plasmons in Strongly Correlated Systems: Spectral Weight Transfer and Renormalized Dispersion
• Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory
• Time Propagation and Spectroscopy of Fermionic Systems Using a Stochastic Technique
• Intermediate coupling model of the cuprates
• Pairing dynamics in strongly correlated superconductivity
• Dynamical mean-field theory for quantum spin systems: Test of solutions for magnetically ordered states
• Two-particle self-consistent approach to unconventional superconductivity
• Σ-Attention: A Transformer-based operator learning framework for self-energy in strongly correlated systems
• Mott physics and spin fluctuations: A functional viewpoint
• Role of frustration and dimensionality in the Hubbard model on the stacked square lattice: Variational cluster approach
• Finite temperature quantum embedding theories for correlated systems
• Mott Insulating States with Competing Orders in the Triangular Lattice Hubbard Model
• Fermion-boson vertex within dynamical mean-field theory
• Mottp-njunctions in layered materials
• Löwdin's symmetry dilemma within Green functions theory for the one‐dimensional Hubbard model
• Mechanism for Orbital Ordering inKCuF3
• Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study
• Absence of Spin Liquid in Nonfrustrated Correlated Systems
• Momentum-space cluster dual-fermion method
• COM(3p) Solution of the 2D Hubbard Model: Momentum-Resolved Quantities
• Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
• Approximate expression for the ground-state energy of the two- and three-dimensional Hubbard model at arbitrary filling obtained from dimensional scaling
• Behavior of Floquet Topological Quantum States in Optically Driven Semiconductors
• Suppression ofd-wave superconductivity in the checkerboard Hubbard model
• Correlated band structure of NiO, CoO, and MnO by variational cluster approximation