Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice

Abstract

Here we analyze the divergences of the irreducible vertex function in dynamical mean field theory, which may indicate either a non-physical breakdown of the perturbation theory or a response to some physical phenomenon. To investigate this question, we construct a quasiparticle vertex from the diverging irreducible vertex functions. This vertex describes the scattering between quasiparticles and quasiholes in a Fermi liquid. We show that the quasparticle vertex \textit{does not} diverge in the charge channel, wherein the irreducible vertex \textit{does} diverge; and we show that the quasiparticle vertex does diverge in the spin channel, wherein the irreducible vertex does not diverge. This divergence occurs at the Mott transition wherein the Fermi liquid theory breaks down. Both Hubbard and Anderson lattices are investigated. In general, our results support that the divergences of the irreducible vertex function do not indicate a non-physical failure of the perturbation theory. Instead, the divergences are the mathematical consequence of inverting a matrix (the local charge susceptibility) which accumulates increasingly negative diagonal elements as the Hubbard interaction suppresses charge fluctuations. Indeed, we find that the first symmetric divergences of the irreducible vertex in both Hubbard and Anderson lattices occurs near the maximum magnitude of the (negative) vertex-connected part of the charge susceptibility, which suppresses charge fluctuations.

References in corpus (22)

• Continuous-time Monte Carlo methods for quantum impurity models
• Renormalization Group Approach to Interacting Fermions
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations
• Breakdown of traditional many-body theories for correlated electrons
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Ab initio dynamical vertex approximation
• The magnetic excitation spectra in BaFe${}_2$As${}_2$: a two-particle approach within DFT+DMFT
• Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a DMFT Perspective
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Is the Mott transition relevant to f-electron metals ?
• T=0 heavy fermion quantum critical point as an orbital selective Mott transition
• Parquet decomposition calculations of the electronic self-energy
• Single-boson exchange decomposition of the vertex function
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Mott transitions in the Periodic Anderson Model

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