Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

Abstract

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.

References in corpus (58)

• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• Continuous Time Quantum Monte Carlo method for fermions
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• First principles approach to the electronic structure of strongly correlated systems: combining GW and DMFT
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene
• Extended Dynamical Mean Field Theory and GW method
• Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model
• Non Fermi Liquid Behaviour near a $T=0$ spin-glass transition
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Spatial Correlations in Dynamical Mean Field Theory
• Diagrammatic Monte Carlo
• Mott physics and spin fluctuations: a unified framework
• Dual boson approach to collective excitations in correlated fermionic systems
• Diagrammatic Monte Carlo for Correlated Fermions
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Efficient perturbation theory for quantum lattice models
• Effective action approach to strongly correlated fermion systems
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Dynamical Screening in Correlated Electron Materials
• When strong correlations become weak: Consistent merging of $GW$ and DMFT
• Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory
• Mott physics and spin fluctuations: a functional viewpoint
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion
• Consistent partial bosonization of the extended Hubbard model
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
• Charge ordering and correlation effects in the extended Hubbard model
• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems
• Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory
• Competing Coulomb and electron-phonon interactions in NbS${}_2$
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Diagrammatic Monte Carlo 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
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Charge order and antiferromagnetism in the extended Hubbard model
• Effective Heisenberg model and exchange interaction for strongly correlated systems
• From local to non-local correlations: the Dual Boson perspective
• Charge ordering and non-local correlations in the doped extended Hubbard model
• Role of three-particle vertex within dual fermion calculations
• Dual Boson approach with instantaneous interaction
• Metal-insulator transition in the 2D Hubbard model: dual fermion approach with the Lanczos exact diagonalization
• Effective Ising model for correlated systems with charge ordering
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Quantum spin fluctuations and evolution of electronic structure in cuprates
• Momentum-Space Cluster Dual Fermion Method
• Direct sampling of the self-energy with Connected Determinant Monte Carlo

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• The half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
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• CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model
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• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
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• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
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