论文标题
荷斯坦模型中非线性电子偶联和顶点校正的相对重要性
Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
论文作者
论文摘要
确定Migdal对电子phonon（$ e $ ph）耦合系统的有效性范围是一个长期的问题。许多尝试回答这个问题的尝试采用了荷斯坦汉密尔顿人，在那里电子密度与局部晶格位移线性伴侣。但是，当这些位移很大时，还必须包括对相互作用的非线性校正，这可以显着改变从该模型获得的物理图片。使用行列式量子蒙特卡洛和自洽的migdal近似，我们比较了荷斯坦模型中具有和没有二阶非线性相互作用的荷斯坦模型中的超导和电荷密度波相关性。我们发现这两种情况之间存在分歧，即使对于$ e $ ph耦合强度的相对较小的值，而且重要的是，这可以发生在Migdal近似值的相同参数区域中。我们的结果表明，有关Migdal近似值的有效性的问题与线性$ E $ ph相互作用的有效性有关。
Determining the range of validity of Migdal's approximation for electron-phonon ($e$-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the $e$-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal's approximation holds. Our results demonstrate that questions regarding the validity of Migdal's approximation go hand in hand with questions of the validity of a linear $e$-ph interaction.
