Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study

Abstract

In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band-edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation (D$\Gamma$A), to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps, through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth, but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchange-driven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.

33 pages, 15 figures

References in corpus (22)

• The density-matrix renormalization group in the age of matrix product states
• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Criticality in Heavy Fermion Metals
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model
• Fate of the false Mott-Hubbard transition in two dimensions
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Nature of magnetic excitations in superconducting BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• The Hubbard model within the equations of motion approach
• Parquet decomposition calculations of the electronic self-energy
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Dynamical vertex approximation for nanoscopic systems
• Correlated starting points for the functional renormalization group
• Underdoped cuprates phenomenology in the 2D Hubbard model within COM(SCBA)
• On the separability of dynamical and non-local correlations in three dimensions
• Competing d-Wave and p-Wave Spin-Singlet Superconductivities in the Two-Dimensional Kondo Lattice
• Composite Operator Method analysis of the underdoped cuprates puzzle

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