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arXiv 2303.02102cond-mat.mtrl-scicond-mat.other
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电子与声子的平衡与非平衡 {\em ab initio} 理论

In- and out-of-equilibrium {\em ab initio} theory of electrons and phonons

Gianluca Stefanucci, Robert van Leeuwen, Enrico Perfetto

AI总结:

本文建立了任意温度下电子与声子的平衡与非平衡 {\em ab initio} 多体量子理论,通过格林函数图解分析推导出 Hedin 方程的有限温度非平衡扩展及 Kadanoff-Baym 方程,并证明了 conserving approximations 的重要性。

摘要:

我们建立了任意温度下平衡与非平衡态电子与声子的 {\em ab initio} 多体量子理论。我们首先解决谐振近似下 {\em ab initio} 哈密顿量的基本问题,证明其必须 {\em 自洽} 地确定以避免不一致性。在确定了最合适的“非相互作用”和“相互作用”部分的划分后,我们进行了格林函数图解分析。我们挑选出关键的图解结构,以用 dressed propagators 和 screened interaction 进行展开。最终结果是 Hedin 方程的有限温度非平衡扩展,其特征是电子自能中出现时间局部的 Ehrenfest 图。Hedin 方程对驱动系统的实时模拟具有有限的实用性。我们利用图解展开的多功能性,生成了格林函数与原子位移的 integro-differential 方程的闭合系统。这些是电子与声子的 Kadanoff-Baym 方程。图解推导的另一个优点是能够使用 conserving approximations,确保时间演化过程中满足所有基本守恒定律。例如,我们证明绝热 Born-Oppenheimer 近似不是 conserving 的,而其动态扩展在电子采用 Fan-Migdal 近似和动态 screened electron-phonon coupling 处理时是 conserving 的。我们还推导了 Kadanoff-Baym 方程在长时间极限和稳态下的形式解。声子格林函数在 quasi-phonon energies 附近的展开表明,在无时间反演不变性的材料中,声子色散可能发生 correlation-induced splitting。

英文摘要:

We lay down the {\em ab initio} many-body quantum theory of electrons and phonons in- and out-of-equilibrium at any temperature. We begin by addressing a fundamental issue concerning the {\em ab initio} Hamiltonian in the harmonic approximation, which we show must be determined {\em self-consistently} to avoid inconsistencies. After identifying the most suitable partitioning into a ``noninteracting'' and an ``interacting'' part we embark on the Green's function diagrammatic analysis. We single out key diagrammatic structures to carry on the expansion in terms of dressed propagators and screened interaction. The final outcome is the finite-temperature nonequilibrium extension of the Hedin equations, featuring the appearance of the time-local Ehrenfest diagram in the electronic self-energy. The Hedin equations have limited practical utility for real-time simulations of driven systems. We leverage the versatility of diagrammatic expansion to generate a closed system of integro-differential equations for the Green's functions and nuclear displacements. These are the Kadanoff-Baym equations for electrons and phonons. Another advantage of the diagrammatic derivation is the ability to use conserving approximations, which ensure the satisfaction of all fundamental conservation laws during the time evolution. As an example we show that the adiabatic Born-Oppenheimer approximation is not conserving whereas its dynamical extension is conserving provided that the electrons are treated in the Fan-Migdal approximation with a dynamically screened electron-phonon coupling. We also derive the formal solution of the Kadanoff-Baym equations in the long time limit and at the steady state. The expansion of the phononic Green's function around the quasi-phonon energies points to a possible correlation-induced splitting of the phonon dispersion in materials with no time-reversal invariance.

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