论文标题
二维Su-Schrieffer-Heeger-Heeger-Hubbard模型的功能重归其化组研究
A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model
论文作者
论文摘要
我们使用奇异模式功能重新归一化组方法研究了与光学Su-Schrieffer-Heeger（SSH）声子外，还研究了在方格上的Hubbard模型。在半填充时，在没有哈伯德相互作用$ u $的情况下，我们找到了退化的旋转密度波（SDW）/电荷 - 密度 - 波（CDW）/S-WAVE超导性（SSC）状态，处于较小的Electron-Phonon耦合强度$λ$和较高的Phonon频率$ $ $ω$和VBS $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。打开正$ U $后，VBS状态被抑制，而SDW状态得到增强。在有限的掺杂，发现SSH声子在$ u = 0 $中偏爱SSC。随着正$ U $的增加，我们发现D-Wave超导率（DSC）和SDW状态不超增量。在中等$ u $和$λ$的狭窄窗口中，我们还找到了不兑换的VBS状态。这里的SSC和DSC可以与CDW和SDW波动自然相关，这两者都可以由SSH声子触发。相比之下，排斥相互作用$ u $增强了SDW，但抑制了CDW波动。我们的一半填充结果与量子蒙特卡洛（QMC）一致，并在有限掺杂时提供洞察力，QMC可能会遭受减去符号问题的困扰。
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 $λ$ and higher phonon frequency $ω$, and the valence bond solid (VBS) state at larger $λ$ and lower $ω$. 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 $λ$, 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.
