用梯度下降法和拟牛顿法从任意波函数逼近全组态相互作用基态
Approaching the Full Configuration Interaction Ground State from an Arbitrary Wavefunction with Gradient Descent and Quasi-Newton Algorithms
摘要：
我们考虑梯度下降和拟牛顿算法优化全组态相互作用（FCI）基态波函数从任意参考态$|0 \rangle$。我们表明，沿优化路径获得的能量可以评估的期望值的$|0 \rangle$，从而避免显式存储的中间波函数。这使我们能够找到的FCI算法的前几个步骤后，系统的能量远远大于什么标准，确定性FCI代码可以处理目前。我们展示了一个应用程序的算法与参考波函数构造为非正交行列式的线性组合。
英文摘要：
We consider gradient descent and quasi-Newton algorithms to optimize the full configuration interaction (FCI) ground state wavefunction starting from an arbitrary reference state $|0 \rangle$. We show that the energies obtained along the optimization path can be evaluated in terms of expectation values of $|0 \rangle$, thus avoiding explicit storage of intermediate wavefunctions. This allows us to find the energies after the first few steps of the FCI algorithm for systems much larger than what standard, deterministic FCI codes can handle at present. We show an application of the algorithm with reference wavefunctions constructed as linear combinations of non-orthogonal determinants.
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