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

TL;DR

This study uses the functional renormalization group to analyze the phase diagram of the two-dimensional Su-Schrieffer-Heeger-Hubbard model, revealing various competing orders influenced by electron-phonon coupling and Hubbard interaction.

Contribution

It provides a comprehensive phase diagram of the 2D SSH-Hubbard model using the singular-mode functional renormalization group, including effects of doping and interactions.

Findings

Identifies SDW, CDW, s-wave and d-wave superconductivity, VBS states depending on parameters.

Shows positive U enhances SDW and suppresses CDW, influencing the phase competition.

Finds SSH phonons favor sSC at zero U and dSC at finite U, with incommensurate states at moderate interactions.

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.