Hubbard模型中太阳能转换的有效Magnus型积分器
Efficient Magnus-type integrators for solar energy conversion in Hubbard models
摘要：
固体中强相互作用的电子一般由Hubbard型模型描述，太阳光的影响可以通过额外的时间依赖性来建模。这就产生了一个有限维的薛定谔型常微分方程（ODE）系统，它可以用Magnus型指数时间积分器数值求解。可以通过将这些与算子分裂相结合来提高效率。我们将讨论几种不同的方法，采用指数为基础的方法结合自适应Lanczos方法评估矩阵指数，并比较其准确性和效率。对于每个积分器，我们使用基于缺陷的局部误差估计，使自适应时间步进。这有助于可靠地控制近似误差并减少计算量
英文摘要：
Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential equations (ODE)s of Schrödinger type, which can be solved numerically by exponential time integrators of Magnus type. The efficiency may be enhanced by combining these with operator splittings. We will discuss several different approaches of employing exponential-based methods in conjunction with an adaptive Lanczos method for the evaluation of matrix exponentials and compare their accuracy and efficiency. For each integrator, we use defect-based local error estimators to enable adaptive time-stepping. This serves to reliably control the approximation error and reduce the computational effort
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