精确分解的非绝热微扰理论
Non-adiabatic perturbation theory of the exact factorisation
AI总结：
本文提出一种新颖的非绝热微扰理论（NAPT），通过将精确分解框架中的电子-核关联项作为微扰处理，证明了其保持归一化和规范协变性，并成功应用于计算 Jahn-Teller 系统的 BO Berry 相位非绝热修正。
摘要：
我们提出了一种新颖的非绝热微扰理论（NAPT），用于处理超越 Born-Oppenheimer（BO）近似的电子与原子核关联系统。该方法的本质是利用电子与核质量比的微小性，将精确分解（EF）框架电子运动方程中的电子-核关联项作为微扰处理。我们证明了 NAPT 的任意有限阶截断均能保持条件电子因子的归一化，以及所得微扰运动方程的规范协变性。我们通过计算具有圆锥交叉的 Jahn-Teller 系统中 BO Berry 相位的非绝热修正，展示了 NAPT 的实用性。它通过最低阶 NAPT 很好地捕捉到了精确 Berry 相位偏离拓扑性质的过程。通过用恒定间隙消除圆锥交叉，它进一步得出了 Berry 相位趋于零的正确标度。
英文摘要：
We present a novel nonadiabatic perturbation theory (NAPT) for correlated systems of electrons and nuclei beyond the Born-Oppenheimer (BO) approximation. The essence of the method is to exploit the smallness of the electronic-to-nuclear mass ratio by treating the electron-nuclear correlation terms in the electronic equation of motion of the exact factorisation (EF) framework as perturbation. We prove that any finite-order truncation of the NAPT preserves the normalisation of the conditional electronic factor as well as the gauge covariance of the resulting perturbative equations of motion. We illustrate the usefulness of NAPT by obtaining nonadiabatic corrections to the BO Berry phase in Jahn--Teller systems with a conical intersection. It well captures the departure of the exact Berry phase from being topological via the lowest-order NAPT. By removing the conical intersection with a constant gap, it further yields the correct scaling of the Berry phase toward zero.
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