Generalized Fourth-Order Decompositions of Imaginary Time Path Integral:Implications of the Harmonic Oscillator  

虚时路径积分的广义四阶拆分方法及其谐振子分析

作　　者：Cong Wang Lihan Zhang Jian Liu Jiushu Shao 王聪;张立涵;刘剑;邵久书(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)

机构地区：[1]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 [2]Institute of Condensed Matter and Material Physics,School of Physics,Peking University,Beijing 100871,China [3]Beijing National Laboratory for Molecular Sciences,Institute of Theoretical and Computational Chemistry,College of Chemistry and Molecular Engineering,Peking University,Beijing 100871,China

出　　处：《Chinese Journal of Chemical Physics》2022年第3期516-536,I0003,共22页化学物理学报（英文）

基　　金：supported by the National Natural Science Foundation of China(No.21961142017,No.22073009 and No.21421003);the Ministry of Science and Technology of China(No.2017YFA0204901)。

摘　　要：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.

关 键 词：Path integral DECOMPOSITION Partition function Harmonic oscillator 

分 类 号：O414.1[理学—理论物理]