The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model

Abstract

The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted to small cluster sizes or rely on various simplifying approximations. We have recently shown that the bosonization of the parquet diagrams provides interpretative and algorithmic advantages over the original purely fermionic formulation. Here we present first results of the numerical implementation of this method by applying it to the half-filled Hubbard model on the square lattice at weak coupling. The improved algorithmic performance allows us to evaluate the parquet approximation for a $16\times 16$ lattice, retaining the full momentum and frequency structure of the various vertex functions. We discuss their symmetries and consider parametrizations of their momentum dependence using the truncated unity approximation.

arXiv comment10 pages, 8 figures

References in corpus (41)

• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• First principles approach to the electronic structure of strongly correlated systems: combining GW and DMFT
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Local Electronic Correlation at the Two-Particle Level
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Mott physics and spin fluctuations: a unified framework
• From infinite to two dimensions through the functional renormalization group
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections
• High-performance functional renormalization group calculations for interacting fermions
• Ab initio dynamical vertex approximation
• Multiloop functional renormalization group that sums up all parquet diagrams
• Multiloop functional renormalization group for general models
• Covalency, double-counting and the metal-insulator phase diagram in transition metal oxides
• Parquet approximation for the 4x4 Hubbard cluster
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Truncated Unity Parquet Solver
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Single-boson exchange decomposition of the vertex function
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Boson-Exchange Parquet Solver for dual fermions
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Thermodynamically consistent description of criticality in models of correlated electrons
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Vertex corrections for positive-definite spectral functions of simple metals
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Real-space cluster dynamical mean-field theory: Center focused extrapolation on the one- and two particle level
• Local Self-Energy Approach For Electronic Structure Calculations
• Enumeration of many-body skeleton diagrams
• Counting Feynman diagrams via many-body relations