Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions

Abstract

Recently, Kozik, Ferrero and Georges have discovered numerically that for a family of fundamental models of interacting fermions, the self-energy $\Sigma [G]$ is a multi-valued functional of the fully dressed single-particle propagator G, and that the skeleton diagrammatic series ${\Sigma }_{\mathrm{bold}}[G]$ converges to the wrong branch above a critical interaction strength. We consider the zero space-time dimensional case, where the same mathematical phenomena appear from elementary algebra. We also find a similar phenomenology for the fully bold formalism built on fully dressed single-particle propagator and pair propagator.

References in corpus (6)

• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Diagrammatic Monte Carlo method for many-polaron problems
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Bold Diagrammatic Monte Carlo technique for frustrated spin systems

Cited by in corpus (36)

• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Breakdown of traditional many-body theories for correlated electrons
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Parquet decomposition calculations of the electronic self-energy
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• The self-consistent Dyson equation and self-energy functionals: failure or new opportunities?
• Unphysical Discontinuities in GW Methods
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices
• Renormalized perturbation theory at large expansion orders
• A similarity renormalization group approach to Green's function methods
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Multi-valuedness of the Luttinger-Ward functional in the Fermionic and Bosonic System with Replicas
• Renormalization group flow of the Luttinger-Ward functional: conserving approximations and application to the Anderson impurity model
• Complex Adiabatic Connection: a Hidden Non-Hermitian Path from Ground to Excited States
• Excitations and spectra from equilibrium real-time Green's functions
• Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators
• Strange Metal Solution in the Diagrammatic Theory for the $2d$ Hubbard Model
• Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
• Thermodynamic Stability at the Two-Particle Level
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• On Green's function embedding using sum-over-pole representations
• Causal optimization method for imaginary-time Green's functions in interacting electron systems
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Thermal quasi-particle theory
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Inchworm tensor train hybridization expansion quantum impurity solver
• Non-perturbative effects of short-range spatial correlations at the two-particle level