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.

11 pages, 5 figures

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• 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