We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state, and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Ref. [arXiv:1403.2968]. We show that choosing a homogeneous ground state solution leads to unstable dynamics for a sufficiently strong interaction, and that allowing a symmetry-broken state prevents this. The instability is caused by the bifurcation of the ground state and understood physically to be connected with the bipolaronic crossover of the exact system. This mean-field instability persists in the partially self-consistent Born approximation but is not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This functions amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid, and how they fail to describe the studied exact properties of the chosen model system.
Phonon-mediated relaxation in nanomaterials from combining Density Functional Theory based non-adiabatic molecular dynamics with Kadanoff-Baym-Keldysh technique
An unified theory of quantised electrons, phonons and photons out-of-equilibrium: a simplified {\em ab-initio} approach based on the Generalised Baym-Kadanoff ansatz
Electronic transport in molecular junctions: The generalized Kadanoff-Baym ansatz with initial contact and correlations
广义Kadanoff-Baym模型（GKBA）提供了一种计算成本低廉的方法来模拟非平衡格林函数框架内的平衡量子系统。对于有限系统，在传统的GKBA方法中忽略初始相关性的限制最近已经被克服[Phys. Rev. B 98，115148（2018）]。然而，在量子传输的上下文中，初始状态的接触性质，即，连接到体引线的结需要GKBA方法的进一步扩展。在这项工作中，我们制定了一个GKBA计划，其中包括初始相关性的分区自由设置。在实践中，这意味着初始关联和接触的分子结的平衡可以与实时演变分开。通过对嵌入自能的记忆积分进行显式计算，将接触初始状态的信息包含在非平衡计算中，这可以在不影响模拟时间和系统大小的计算缩放的情况下进行。我们展示了碳基分子结，在那里我们研究了瞬态电流签名中的电子相关性的作用开发的方法。
Benchmarking the generalized Kadanoff-Baym ansatz and second-order adiabatic expansion using time-dependent spintronic effects: Spin pumping, torque, and inertia
University of Delaware（特拉华大学）；Universidad Nacional de Colombia（哥伦比亚国立大学）
