论文标题
耦合电子和声子的约束辅助场量子蒙特卡洛
Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
论文作者
论文摘要
我们提出了约束辅助辅助场量子蒙特卡洛（CP-AFQMC）的扩展，用于处理与声子耦合的相关电子系统。该算法遵循标准的CP-AFQMC方法来描述电子自由度，同时用第一次量化描述了声子，并通过扩散的蒙特卡洛方法进行了传播。我们的方法对一维荷尔斯坦和哈伯德 - 荷尔斯坦模型进行了测试。使用简单的半经验试验波函数，对于$ω/（2 \ text {d}tλ）<1 $，对于本研究中考虑的荷尔斯坦模型中的所有参数，我们的方法非常准确。此外，我们从经验上表明，自相关时间尺度为$ 1/ω$，对于$ω/t \ Lessim 1 $，这比$ 1/ω^2 $缩放的常规量子量子carlo garlo算法的缩放是一种改进。在Hubbard-Holstein模型中，当Hubbard $ u $项统治模型的物理学时，我们算法的准确性与Hubbard模型的标准CP-AFQMC的准确性与Hubbard模型的准确性一致，并且何时地面状态被电子量子偶联量表$λ$ up $ c $。这项工作中开发的方法对于理解模型晶格问题和AB-Initio系统中电子和声子之间的相互作用产生的复杂物理学应该是有价值的。
We present an extension of constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) for the treatment of correlated electronic systems coupled to phonons. The algorithm follows the standard CP-AFQMC approach for description of the electronic degrees of freedom while phonons are described in first quantization and propagated via a diffusion Monte Carlo approach. Our method is tested on the one- and two-dimensional Holstein and Hubbard-Holstein models. With a simple semiclassical trial wavefunction, our approach is remarkably accurate for $ω/(2\text{d}tλ) < 1$ for all parameters in the Holstein model considered in this study. In addition, we empirically show that the autocorrelation time scales as $1/ω$ for $ω/t \lesssim 1$, which is an improvement over the $1/ω^2$ scaling of the conventional determinant quantum Monte Carlo algorithm. In the Hubbard-Holstein model, the accuracy of our algorithm is found to be consistent with that of standard CP-AFQMC for the Hubbard model when the Hubbard $U$ term dominates the physics of the model, and is nearly exact when the ground state is dominated by the electron-phonon coupling scale $λ$. The approach developed in this work should be valuable for understanding the complex physics arising from the interplay between electrons and phonons in both model lattice problems and ab-initio systems.
