Dual fermion method as a prototype of generic reference-system approach for correlated fermions

Abstract

We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the same interaction term as the original system. Thereby no restrictions are imposed by the locality of the reference problem or by the nature of the original problem as a lattice one. We present new arguments in favour of keeping the dual denominator in the expression for the lattice self-energy independently of the truncation of the dual interaction. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a $2\times 2$ plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.

References in corpus (30)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Ab initio calculations of quasiparticle band structure in correlated systems: LDA++ approach
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• First principles approach to the electronic structure of strongly correlated systems: combining GW and DMFT
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene
• Extended Dynamical Mean Field Theory and GW method
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Mott physics and spin fluctuations: a unified framework
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Efficient perturbation theory for quantum lattice models
• When strong correlations become weak: Consistent merging of $GW$ and DMFT
• Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation
• Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory
• Mott physics and spin fluctuations: a functional viewpoint
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Cluster Dynamical Mean Field Theories
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Superperturbation solver for quantum impurity models
• Role of three-particle vertex within dual fermion calculations
• Capturing non-local interaction effects in the Hubbard model: optimal mappings and limits of applicability
• The effect of six-point one-particle reducible local interactions in the dual fermion approach
• Local correlation functions of arbitrary order for the Falicov-Kimball model
• Exactly solvable model of strongly correlated $d$-wave superconductivity
• Interlaced coarse-graining for the dynamic cluster approximation
• A new approach to strongly correlated fermion systems: the spin-particle-hole coherent-state path integral
• Continuous momentum dependence in the dynamical cluster approximation

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• Non-Fermi-liquid behaviour and Fermi-surface expansion induced by van Hove-driven ferromagnetic fluctuations: the D-TRILEX analysis
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