Ten Brink M, Gräber S, Hopjan M, Jansen D, Stolpp J, Heidrich-Meisner F, Blöchl P E
Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
J Chem Phys. 2022 Jun 21;156(23):234109. doi: 10.1063/5.0092063.
We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.
通过研究荷斯坦模型中的实时动力学，我们将一组量子化学方法（包括多轨迹埃伦费斯特方法、最少开关表面跳跃方法和多组态埃伦费斯特动力学方法）与精确的量子多体技术进行了基准测试。这是凝聚态理论中的一个典型模型，它包含电子与爱因斯坦声子的局部耦合。对于两格点和三格点的荷斯坦模型，我们根据玻恩 - 黄形式论讨论了精确方法和量子化学方法，涵盖了不同的初始态，这些初始态要么从单个玻恩 - 奥本海默表面开始，要么电子局域在单个格点上。对于多达51个格点的扩展系统，我们研究了单个荷斯坦极化子的物理性质以及有限电子密度下电荷密度波的动力学。对于这些扩展系统，我们将量子化学方法与通过具有局部基优化的含时密度矩阵重整化群计算（DMRG - LBO）得到的精确动力学进行了比较。我们观察到，一般来说，多轨迹埃伦费斯特方法仅能准确捕捉超短时间的动力学。相比之下，经过适当修正的表面跳跃方法能更好地描述长时间行为，但在描述不同玻恩 - 奥本海默态之间的短时间相干性方面存在困难。我们表明，多组态埃伦费斯特方法相对于多轨迹埃伦费斯特方法有显著改进，并且在适度的计算量下，在小系统中可以收敛到精确结果。我们还进一步观察到，对于扩展系统，这种收敛相对于组态数量来说较慢。我们的基准测试研究表明，DMRG - LBO是评估量子化学方法质量的一个有用工具。
