论文标题
来自耦合费米子“僵尸”状态想象时间演变的电子能量
Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution
论文作者
论文摘要
僵尸状态是最近引入的形式主义，用于描述以计算方式解决费米子符号问题的耦合相干的效费状态。以前已经表明，具有旋转轨道分数职业的僵尸状态遵守了正确的效率创造和an灭代数，并提出了实时进化的结果[Dmitrii V. Shalashilin，J。Chem。物理。 148，194109（2018）]。在这项工作中，我们通过开发有效的算法来评估僵尸国家之间的哈密顿和其他运营商并解决其正常化，从而扩展并建立在这种形式主义的基础上。我们还展示了如何使用假想的时间传播来找到系统的基态。我们还提出了一种偏见的方法，用于建立一组随机僵尸状态，该方法可以使用较小的基础尺寸，同时仍然准确地描述了Hamiltonian及其基态的电子结构，并描述了波函数“清洁”的技术，从而消除了具有错误的电子数量的配置的贡献，从而进一步改进了准确的精度。我们还展示了如何使用革兰氏链式正交程序可以有效地计算低较低的激发态。在僵尸状态的有偏见的随机网格上，提出的想象时间传播的算法可能是现有量子蒙特卡洛方法的替代方法。
Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner. Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution [Dmitrii V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods.
