Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs

Abstract

We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes non-local effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between band-like weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle.

15 pages, 15 figures Second version + minor changes

References in corpus (24)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Quantum Cluster Theories
• LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}
• Continuous Time Quantum Monte Carlo method for fermions
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• Renormalization group analysis of the 2D Hubbard model
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• d-wave Superconductivity in the Hubbard Model
• Pseudogap and antiferromagnetic correlations in the Hubbard model
• One-Particle an Two-Particle Instability of Coupled Luttinger Liquids
• Robustness of the van Hove scenario for high-Tc superconductors
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Effects of the Van Hove singularities on magnetism and superconductivity in the t-t' Hubbard model: a parquet approach
• Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework
• Non-local Coulomb interactions and metal-insulator transition in Ti${}_2$O${}_3$: a cluster LDA+DMFT approach
• Fermi Surface and Electron Correlation Effects of Ferromagnetic Iron
• Dynamical Mean Field Theory of the Antiferromagnetic Metal to Antiferromagnetic Insulator Transition
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• The superconducting gap in the Hubbard model and the two gap energy scales in high-Tc cuprates
• Strong Coupling Theory for Interacting Lattice Models
• Bond excitations in the pseudogap phase of the Hubbard Model
• Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems

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