Dynamical vertex approximation for the attractive Hubbard model

Abstract

In this work, we adapt the formalism of the dynamical vertex approximation (D$\Gamma$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$\Gamma$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models. It will be shown, how this property can be related to the structure of the ladders, which makes our derivation applicable for any approximation scheme based on ladder diagrams. Finally, we apply our D$\Gamma$A algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, we focus on the parameters region in the proximity of the second-order transition to the superconducting and charge-density wave phases, respectively, and calculate (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties.

References in corpus (14)

• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of Bose-Einstein Condensation of Molecules
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Ab initio dynamical vertex approximation
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Competing superfluid and density-wave ground-states of fermionic mixtures with mass imbalance in optical lattices
• Polarized superfluidity in the attractive Hubbard model with population imbalance
• The extended Hubbard model with attractive interactions

Cited by in corpus (25)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Truncated Unity Parquet Solver
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Boson-Exchange Parquet Solver for dual fermions
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Quantum criticality in the two-dimensional periodic Anderson model
• How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems
• Dual Boson approach with instantaneous interaction
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Strongly correlated superconductivity with long-range spatial fluctuations
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Anisotropy of electronic correlations: On the applicability of local theories to layered materials
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures
• Consistency of potential energy in the dynamical vertex approximation
• Coexistence of $s$-wave superconductivity and phase separation in the half-filled extended Hubbard model with attractive interactions
• General Shiba mapping for on-site four-point correlation functions
• Second-order phase transitions and divergent linear response in dynamical mean-field theory
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• The non-analytic momentum dependence of spin susceptibility of Heisenberg magnets in paramagnetic phase and its effect on critical exponents
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory