Electron-Phonon Interactions in Flat Band Systems

Abstract

Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO${}_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave (CDW) phases at one-third and two-thirds fillings, characterized by long-range density density correlations between doubly occupied sites on the minority or majority sublattice, and an accompanying gap. We also compute the transition temperature to the ordered phase as a function of the electron-phonon coupling.

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• Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• The half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
• Bose-Einstein condensation in honeycomb dimer magnets and $\mathrm{Y}{\mathrm{b}}_2\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_7$
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Charge Singlets and Orbital-Selective Charge Density Wave Transitions
• Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential
• Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Tuning superconductivity and charge density wave order by next-nearest-neighbor hopping integral in honeycomb Holstein model