论文标题
适用于各向异性fröhlich模型的变分极化方程
Variational Polaron Equations Applied to the Anisotropic Fröhlich Model
论文作者
论文摘要
从极化物的第一原理建模的最新进展开始，在Bloch空间中，强耦合绝热近似中的变异极化子方程是在极偶联的。在此框架中，获得了极性地层的能量以及单个电子，声子和电子形成贡献。我们建议一种有效的基于梯度的优化算法，并将这些方程应用于具有各向异性非脱位电子带的广义Fröhlich模型，包括两维情况。 Fröhlich电子 - Phonon矩阵元素在$γ$ - 点的差异的影响得到了分析处理，从而改善了相对于相互空间中的采样的收敛性。通过在各向同性场景中获得标准fröhlich模型的已知渐近解决方案，以及通过将我们的结果与高斯ANSATZ方法进行比较，从而验证了整个方法，从而显示了数值精确的和高斯试验波形之间的差异。此外，将能量分解为单个术语，使人们可以恢复Pekar的1：2：3：4定理，即使在各向异性情况下，该定理也被证明是有效的。我们预计形式主义和数值实施的改进将适用于Fröhlich模型固有的大型二极管假设。
Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fröhlich model with anisotropic non-degenerate electronic bands, both in two- and three-dimensional cases. The effect of the divergence of Fröhlich electron-phonon matrix elements at $Γ$-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fröhlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fröhlich model.
