动态平均场论计算的收敛加速和稳定化
Convergence acceleration and stabilization for dynamical-mean-field-theory calculations
摘要：
在关联电子系统模型的动力学平均场论（DMFT）计算中，通过适当地混合杂化函数，可以显著地加速收敛到自洽性。结果表明，密度泛函理论（DFT）计算中输入电荷密度混合的技术和过去的经验在DMFT中也是有效的。作为一个例子，在哈伯德模型中，由于临界慢化而导致的Mott金属-绝缘体相变附近计算量的增加，可以通过使用改进的Broyden方法数值求解非线性自洽方程而大大减少。在实际计算中观察到高达3的加速因子，即使对于这个相对表现良好的问题。此外，收敛可以在困难的情况下实现，其中简单的线性混合是无效的，甚至导致发散。也可以得到不稳定和亚稳定的溶液。我们还确定了系统的线性响应相对于杂交函数的变化，这是相关的不同的能量尺度之间的信息在迭代过程中的传播。
英文摘要：
The convergence to the self-consistency in the dynamical-mean-field-theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver. It is shown that the techniques and the past experience with the mixing of input charge densities in the density-functional-theory (DFT) calculations are also effective in DMFT. As an example, the increase of the computational requirements near the Mott metal-insulator transition in the Hubbard model due to critical slowing down can be strongly reduced by using the modified Broyden's method to numerically solve the non-linear self-consistency equation. Speed-up factors as high as 3 were observed in practical calculations even for this relatively well behaved problem. Furthermore, the convergence can be achieved in difficult cases where simple linear mixing is either not effective or even leads to divergence. Unstable and metastable solutions can also be obtained. We also determine the linear response of the system with respect to the variations of the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.
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