A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model

Abstract

We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half-filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave (SDW)/charge-density-wave (CDW)/s-wave superconductivity (sSC) state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at $U=0$. With increasing positive $U$, we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC), and provide insights at finite doping where QMC may suffer from the minus sign problem.

12 pages, 7 figures

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• Cooperation between electron-phonon coupling and electronic interaction in bilayer nickelates La${}_3$Ni${}_2$O${}_7$
• Bipolaronic superconductivity out of a Coulomb gas
• Ground state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model
• Resonating Valence Bond States in an Electron-Phonon System
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Electronic orders on the kagome lattice at the lower Van Hove filling
• Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
• Strain-Engineered Electronic Structure and Superconductivity in La${}_3$Ni${}_2$O${}_7$ Thin Films
• Charge bond order and s-wave superconductivity in the kagome lattice with electron-phonon coupling and electron-electron interaction
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Anomalous isotope Effect in d-wave superconductors on the square lattice
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization