The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems

Abstract

We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input of two-particle irreducible functional renormalization-group (2PI-fRG) approach. Using 2PI-fRG approach allows us to treat both, local and non-local interactions. In case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMF${}^2$RG approach. In a simplest truncation, neglecting scale-dependence of the two-particle irreducible vertices, we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual boson or D$\Gamma$A approach; in more sophisticated truncations the method allows us to consider non-local corrections to the self-energy, as well as the interplay of charge- and spin correlations. treatment of vertex renormalizations. The proposed scheme is tested on the two-dimensional standard and extended $U$-$V$ half-filled Hubbard models. For the standard Hubbard model we obtain non-local self-energy, which is in agreement with numerical studies; for the extended Hubbard model we obtain the boundary of charge instability, which agrees well with the results of the dual boson (DB) approach. We also find that the effect of spin correlations on electron interaction in the charge channel, not considered previously in the DB approach, only slightly reduces critical next-nearest-neighbor interaction of charge instability of the extended Hubbard model at the considered finite small temperature, yielding better agreement with dynamic cluster approximation. The considered method is rather general and can be applied to study various phenomena in strongly-correlated electronic systems.

31 pages, 5 figures

References in corpus (28)

• Theory of Intertwined Orders in High Temperature Superconductors
• Calculations of Hubbard U from first-principles
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Screened Coulomb interaction in the maximally localized Wannier basis
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Breakdown of traditional many-body theories for correlated electrons
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Ab initio dynamical vertex approximation
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Interaction flow method for many-fermion systems
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Charge ordering and correlation effects in the extended Hubbard model
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory
• Correlated starting points for the functional renormalization group
• From local to non-local correlations: the Dual Boson perspective
• $i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Two-particle irreducible functional renormalization group schemes---a comparative study
• The effect of six-point one-particle reducible local interactions in the dual fermion approach

Cited by in corpus (19)

• The nonperturbative functional renormalization group and its applications
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Consistent partial bosonization of the extended Hubbard model
• 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
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Multiloop flow equations for single-boson exchange fRG
• divERGe implements various Exact Renormalization Group examples
• Improved treatment of fermion-boson vertices and Bethe-Salpeter equations in non-local extensions of dynamical mean field theory
• Stochastic pole expansion method
• Multi-channel fluctuating field approach to competing instabilities in interacting electronic systems
• Electronic correlations and long-range magnetic ordering in NiO tuned by pressure
• Coexistence of $s$-wave superconductivity and phase separation in the half-filled extended Hubbard model with attractive interactions
• Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• 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
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Dynamical Cluster Approximation Study of Electron Localization in the Extended Hubbard Model