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arXiv 2211.04089cond-mat.str-elcond-mat.stat-mechphysics.chem-phphysics.comp-phquant-ph
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利用层级运动方程方法对费米子库进行高效低温模拟:应用于安德森杂质模型

Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model

Xiaohan Dan, Meng Xu, J. T. Stockburger, J. Ankerhold, Qiang Shi

AI总结:

本文提出用重心有理分解近似费米函数和杂化函数,大幅减少HEOM方法中库关联函数分解所需基函数数量,从而实现对费米子库超低温高效精确模拟,并在安德森杂质模型上验证了方法的效率、精度和长时间稳定性。

摘要:

层级运动方程(HEOM)方法是一种精确模拟开放系统量子动力学的方法,它允许系统性地收敛到数值精确结果。为了表示库的影响,在HEOM方法中,库关联函数通常被分解为多个指数项的求和。由于库关联函数在低温下或当库具有复杂能带结构时会变得高度非马尔可夫,当前的一个挑战是获得精确的指数分解,以便能够利用HEOM进行高效模拟。在这项工作中,我们采用重心表示在频域中近似费米函数和杂化函数。这种新方法通过使用优化的有理分解来近似这些函数,极大地减少了分解库关联函数时基函数的数量,从而进一步使得HEOM方法能够应用于超低温和一般库结构。我们通过将该新分解方案应用于低温区具有洛伦兹型和紧束缚型杂化函数的安德森杂质模型(AIM),展示了其效率、精度和长时间稳定性。

英文摘要:

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence to numerically exact results. To represent the effects of the bath, the reservoir correlation functions are usually decomposed into the summation of multiple exponential terms in the HEOM method. Since the reservoir correlation functions become highly non-Markovian at low temperatures or when the bath has complex band structures, a present challenge is to obtain accurate exponential decompositions that allow efficient simulation with the HEOM. In this work, we employ the barycentric representation to approximate the Fermi function and hybridization functions in the frequency domain. The new method, by approximating these functions with optimized rational decomposition, greatly reduces the number of basis functions in decomposing the reservoir correlation functions, which further allows the HEOM method to be applied to ultra-low temperature and general bath structures. We demonstrate the efficiency, accuracy, and long-time stability of the new decomposition scheme by applying it to the Anderson impurity model (AIM) in the low-temperature regime with the Lorentzian and tight-binding hybridization functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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