Constrained-path auxiliary-field quantum Monte Carlo for coupled electrons and phonons
Constrained-path auxiliary-field quantum Monte Carlo for coupled electrons and phonons
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DOI：
10.1103/physrevb.103.115123
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发表时间：
2020-12
影响因子：
3.7
通讯作者：
Joonho Lee;Shiwei Zhang;D. Reichman
中科院分区：
文献类型：
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作者：
Joonho Lee;Shiwei Zhang;D. Reichman
本文提出了一种扩展的约束路径非相干场量子蒙特卡罗方法（CP-AFQMC），用于处理与声子耦合的关联电子系统。该算法遵循标准的CP-AFQMC方法描述的电子自由度，而声子描述在第一量子化和传播通过扩散蒙特卡罗方法。我们的方法进行了测试的一维和二维Holstein和Hubbard-Holstein模型。用一个简单的半经典试验波函数，我们的方法是非常准确的$\omega/（2\text{d}t\lambda）< 1$的所有参数在这项研究中考虑的Holstein模型。此外，我们的经验表明，自相关时间尺度为1/\omega$为$\omega/t \lesssim 1$，这是一个改进的传统的决定性量子蒙特卡罗算法的1/\omega ^2 $标度。在Hubbard-Holstein模型中，当Hubbard $U$项主导模型的物理性质时，我们的算法的精度与标准CP-AFQMC算法的精度一致，当基态由电子-声子耦合尺度$\lambda$主导时，算法的精度接近精确.在这项工作中开发的方法应该是有价值的理解所产生的复杂的物理模型晶格问题和从头算系统中的电子和声子之间的相互作用。
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 $\omega/(2\text{d}t\lambda) < 1$ for all parameters in the Holstein model considered in this study. In addition, we empirically show that the autocorrelation time scales as $1/\omega$ for $\omega/t \lesssim 1$, which is an improvement over the $1/\omega^2$ 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 $\lambda$. 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.