Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory

Abstract

We present here two alternative schemes designed to correct the high-frequency truncation errors in the numerical treatment of the Bethe-Salpeter equations. The schemes are applicable to all Bethe-Salpeter calculations with a local two-particle irreducible local, which is relevant, e.g., for the dynamical mean-field theory (DMFT) and its diagrammatic extensions. In particular, within a purely diagrammatic framework, we could extend existing algorithms for treating the static case in the particle-hole sector to more general procedures applicable to all bosonic frequencies and all channels. After illustrating the derivation and the theoretical interrelation of the two proposed schemes, these have been applied to the Bethe-Salpeter equations for the auxiliary Anderson impurity models of selected DMFT calculations, where results can be compared against a numerically "exact" solution. The successful performance of the proposed schemes suggests that their implementation can significantly improve the accuracy of dynamical mean-field theory (DMFT) calculations at the two-particle level, in particular for more realistic multi-orbital calculations where the large number of degrees of freedom substantially restricts the actual frequency range for numerical calculations, as well as -on a broader perspective- of the diagrammatic extensions of DMFT.

arXiv comment20 pages, 12 figures

References in corpus (35)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Quantum Cluster Theories
• Functional renormalization group approach to correlated fermion systems
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
• Local Electronic Correlation at the Two-Particle Level
• Mott physics and spin fluctuations: a unified framework
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Dual boson approach to collective excitations in correlated fermionic systems
• From infinite to two dimensions through the functional renormalization group
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Superconductivity from emerging magnetic moments
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Mott physics and spin fluctuations: a functional viewpoint
• One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Quantum dynamical screening of the local magnetic moment in Fe-based superconductors
• Electronic orders in multi-orbital Hubbard models with lifted orbital degeneracy
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Superperturbation solver for quantum impurity models
• Superconductivity of Composite Particles in Two-Channel Kondo Lattice
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Ab initio calculations with the dynamical vertex approximation
• Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
• Long-range orders, spin- and orbital-freezing in the two-band Hubbard model
• Two-particle-correlations in a functional renormalization group scheme using a dynamical mean-field theory approach

Cited by in corpus (36)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Single-boson exchange decomposition of the vertex function
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• 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
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Efficient evaluation of the polarization function in dynamical mean-field theory
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• 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
• Improved treatment of fermion-boson vertices and Bethe-Salpeter equations in non-local extensions of dynamical mean field theory
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Multipolar ordering from dynamical mean field theory with application to CeB6
• Consistency of potential energy in the dynamical vertex approximation
• Approximating the frequency dependence of the effective interaction in the functional renormalization group for many-fermion systems
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• General Shiba mapping for on-site four-point correlation functions
• Development of an efficient impurity solver in dynamical mean field theory for multi-band systems: The iterative perturbation theory combined with the parquet equations
• Second-order dual fermion for multi-orbital systems
• Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• Disentangling real space fluctuations: the diagnostics of metal-insulator transitions beyond single-particle spectral functions
• Non-perturbative effects of short-range spatial correlations at the two-particle level
• Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory