| 虚时路径积分的广义四阶拆分方法及其谐振子分析 |
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| 引用本文： | 王 聪,张立涵,刘 剑,邵久书.虚时路径积分的广义四阶拆分方法及其谐振子分析[J].化学物理学报,2022(3):516-536. |
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| 作者姓名： | 王 聪 张立涵 刘 剑 邵久书 |
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| 作者单位： | 北京师范大学化学学院，理论及计算光化学教育部重点实验室，高等量子研究中心，北京 100875;北京大学物理学院，凝聚态物理与材料物理研究所，北京 100871;北京大学化学与分子工程学院，理论与计算化学研究所，北京分子科学国家研究中心，北京 100871 |
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| 摘 要： | 虚时路径积分方法是计算实际体系量子热力学性质的有效工具. 本文重点分析讨论了基于二阶和四阶拆分的虚时路径积分的有效性，给出谐振子体系配分函数统一的解析形式，进而得到其热力学性质和主要误差的表达式. 通过去除谐振子配分函数的主要误差，广义对称四阶拆分中的自由参数得以固定，以此计算实际体系的热力学量可以达到期望的三阶精度.
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| 关 键 词： | 路径积分，拆分方法，配分函数，谐振子 |
| 收稿时间： | 2022/5/16 0:00:00 |
Generalized Fourth-Order Decompositions of Imaginary Time Path Integral: Implications of the Harmonic Oscillator |
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| Cong Wang,Lihan Zhang,Jian Liu,Jiushu Shao.Generalized Fourth-Order Decompositions of Imaginary Time Path Integral: Implications of the Harmonic Oscillator[J].Chinese Journal of Chemical Physics,2022(3):516-536. |
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| Authors: | Cong Wang Lihan Zhang Jian Liu Jiushu Shao |
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| Institution: | College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China;Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China;Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China |
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| Abstract: | The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems. We show that, when second-order and fourth-order decompositions are employed, they share a remarkable unified analytic form for the partition function of the harmonic oscillator. We are then able to obtain the expression of the thermodynamic property and the leading error terms as well. In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme, we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system. Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems. |
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| Keywords: | Path integral Decomposition Partition function Harmonic oscillator |
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