用量子关联函数探测非谐声子：路径积分方法
Probing anharmonic phonons by quantum correlators: A path integral approach
摘要：
我们设计了一个有效的方案来确定振动特性的路径积分分子动力学（PIMD）模拟。该方法基于零时间Kubo变换的关联函数，并捕获由于温度和量子效应引起的势的非谐性。使用解析推导和数值计算的玩具模型的潜力，我们表明，两个不同的估计建立在PIMD关联函数充分表征的声子谱和非谐强度。第一个估计器与力-力量子关联函数相关联，并且可以访问量子系统的基频和热力学性质。第二个连接到位移-位移关联函数，并以高精度探测最低能量的声子激发。我们还证明，使用广义本征值方程，在标准的简正模方程，导致显着的加速在PIMD声子计算，无论是在更快的收敛速度和更小的时间步长偏置。在这个框架内，使用从头算PIMD模拟，我们计算的声子分散金刚石和高压I41/amd阶段的原子氢。我们发现，在后一种情况下，非谐性比以前估计的更强，并产生相当大的红移原子氢的振动光谱。
英文摘要：
We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with force-force quantum correlators and gives access to the fundamental frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and probes the lowest-energy phonon excitations with high accuracy. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time-step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that, in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.
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