Electron-phonon interaction in Strongly Correlated Systems

Abstract

The Hubbard-Holstein model is a simple model including both electron-phonon interaction and electron-electron correlations. We review a body of theoretical work investigating the effects of strong correlations on the electron-phonon interaction. We focus on the regime, relevant to high-T_c superconductors, in which the electron correlations are dominant. We find that the electron-phonon interaction can still have important signatures, even if many anomalies appear, and the overall effect is far from conventional. In particular in the paramagnetic phase the effects of phonons are much reduced in the low-energy properties, while the high-energy physics can be strongly affected by phonons. Moreover, the electron-phonon interaction can still give rise to important effects, like phase separation and charge-ordering, and it assumes a predominance of forward scattering even if the bare interaction is assumed to be local (momentum independent). Antiferromagnetic correlations reduce the screening effects due to electron-electron interactions and revive the electron-phonon effects.

15 pages, 12 figures

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• Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons
• Charge instabilities and electron-phonon interaction in the Hubbard-Holstein model
• Superlight small bipolarons
• Bipolarons from long range interactions: Singlet and triplet pairs in the screened Hubbard-Froehlich model on the chain
• Gutzwiller scheme for electrons and phonons: the half-filled Hubbard-Holstein model
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Cited by in corpus (27)

• Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach
• Giant phonon anomalies and central peak due to charge density wave formation in YBa${}_2$Cu${}_3$O${}_{6.6}$
• Cuprate superconductors as viewed through a striped lens
• Dynamical Screening Effects in Correlated Electron Materials -- A Progress Report on Combined Many-Body Perturbation and Dynamical Mean Field Theory: "GW+DMFT"
• The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation
• Highly anisotropic anomaly in the dispersion of the copper-oxygen bond-bending phonon in superconducting YBa2Cu3O7 from inelastic neutron scattering
• Localised vibrations in superconducting YBCO revealed by ultra-fast optical coherent spectroscopy
• Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling
• Downfolding electron-phonon Hamiltonians from ab-initio calculations: application to K${}_3$Picene
• Polaronic Optical Transitions in Hematite ($\alpha -F{e}_2{O}_3$) Revealed by First-Principles Electron-Phonon Coupling
• Density Functional Theory of the Hubbard-Holstein Model
• Competing phases and orbital-selective behaviors in the two-orbital Hubbard-Holstein model
• Constraints on the total coupling strength to bosons in iron based superconductors
• Slave rotor approach to dynamically screened Coulomb interactions in solids
• Influence of correlations on transitive electron-phonon couplings in cuprate superconductors
• Competing Correlated Insulators in multi-orbital systems coupled to phonons
• Role of electron-phonon interaction in a magnetically driven mechanism for superconductivity
• Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
• Next-generation EDIpack: A Lanczos-based package for quantum impurity models featuring general broken-symmetry phases, flexible bath topologies and multi-platform interoperability
• Optical phonons for Peierls chains with long-range Coulomb interactions
• Embedding Dynamical Mean-Field Theory for Superconductivity in Layered Materials and Heterostructures
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Phase separation and pairing fluctuations in oxide materials
• Role of the upper branch of the hour-glass magnetic spectrum in the formation of the main kink in the electronic dispersion of high-T${}_{\text{c}}$ cuprate superconductors
• Electron-phonon coupling in correlated materials: insights from the Hubbard-Holstein model
• Superconductor-Insulator transition in a two-orbital attractive Hubbard model with Hund's exchange
• Axionic $p+is$ superconductivity from two pairing channels