Multi-channel fluctuating field approach to competing instabilities in interacting electronic systems

Abstract

Systems with strong electronic Coulomb correlations often display rich phase diagrams exhibiting different ordered phases involving spin, charge, or orbital degrees of freedom. The theoretical description of the interplay of the corresponding collective fluctuations giving rise to this phenomenology remains however a tremendous challenge. Here, we introduce a multi-channel extension of the recently developed fluctuating field approach to competing collective fluctuations in correlated electron systems. The method is based on a variational optimization of a trial action that explicitly contains the order parameters of the leading fluctuation channels. It gives direct access to the free energy of the system, facilitating the distinction between stable and meta-stable phases of the system. We apply our approach to the extended Hubbard model in the weak to intermediate coupling regime where we find it to capture the interplay of competing charge density wave and antiferromagnetic fluctuations with qualitative agreement with more computationally expensive methods. The multi-channel fluctuation field approach thus offers a promising new route for a numerically cheap treatment of the interplay between collective fluctuations in large systems.

arXiv comment11 pages, 5 figures

References in corpus (48)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Quantum Cluster Theories
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
• Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene
• Tricritical Behavior in the Extended Hubbard Chains
• From band insulator to Mott insulator in one dimension
• Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Mechanism of CDW-SDW Transition in One Dimension
• Quantum critical behavior of the one-dimensional ionic Hubbard model
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Renormalization group flows into phases with broken symmetry
• Charge ordering in extended Hubbard models: Variational cluster approach
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Ab initio dynamical vertex approximation
• Flow Equations without Mean Field Ambiguity
• Consistent partial bosonization of the extended Hubbard model
• Charge ordering and correlation effects in the extended Hubbard model
• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• 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
• Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Charge order and antiferromagnetism in the extended Hubbard model
• From local to non-local correlations: the Dual Boson perspective
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Nearest-Neighbor Repulsion and Competing Charge and Spin Order in the Extended Hubbard Model
• Plaquette Valence Bond Theory of High-Temperature Superconductivity
• Dual Boson approach with instantaneous interaction
• Chiral d-wave Superconductivity in a Triangular Surface Lattice Mediated by Long-range Interaction
• 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
• Towards ab initio calculations with the dynamical vertex approximation
• Collective magnetic fluctuations in Hubbard plaquettes captured by fluctuating local field method
• Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• Analysis of the dynamical cluster approximation for the Hubbard model
• The extended Hubbard model with attractive interactions
• Orientational bond and Néel order in the two-dimensional ionic Hubbard model
• Fluctuating local field method probed for a description of small classical correlated lattices
• Spin and charge modulations of a half-filled extended Hubbard model
• Fluctuating local field approach to free energy of 1D molecules with strong collective electronic correlations
• Collective excitations of a charged Fermi superfluid in the BCS-BEC crossover

Cited by in corpus (4)

• CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model
• Coexistence of $s$-wave superconductivity and phase separation in the half-filled extended Hubbard model with attractive interactions
• Exact functional integration of radial and complex slave-boson fields: thermodynamics and dynamics of the two-site extended Hubbard model
• Charge Collective Modes in Correlated Electron Systems: Plasmons Beyond the Random Phase Approximation