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Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
Physical Review Research Pub Date : 2021-07-23 , DOI: 10.1103/physrevresearch.3.l032017
Jae-Mo Lihm , Cheol-Hwan Park

The anharmonic lattice is a representative example of an interacting, bosonic, many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therein resorts to an ansatz, whose validity has not yet been theoretically proven. Here we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of the time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.

中文翻译:

有限温度非谐晶格动力学的高斯时间相关变分原理

非谐晶格是相互作用的玻色多体系统的典型例子。自洽调和近似已被证明可用于研究非调和晶格的平衡特性。然而,其中动力学性质的研究求助于 ansatz,其有效性尚未在理论上得到证实。在这里,我们将瞬态变分原理(一种最近出现的用于研究相互作用多体系统的动力学特性的有用工具)应用于有限温度下使用高斯态作为变分流形的非调和晶格哈密顿量。我们推导出位置的位置相关函数和所述声子自能的解析公式,证明动力学拟设的自洽调和近似。我们在时间相关变分原理和非谐格哈密顿量之间建立了富有成效的联系,在这两个领域提供了见解。我们的工作扩展了时间相关变分原理对第一性原理格子哈密顿量的适用范围,并为使用全变分框架研究非调和格子的动力学特性奠定了基础。
更新日期:2021-07-23
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