非平衡$GW$近似的实时Dyson展开：关联谱与参考传播子的依赖性
Real-time Dyson expansion for the nonequilibrium $GW$ approximation: Correlated spectra and dependence on the reference propagator
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- Institute for Theoretical Physics and Astrophysics, Kiel University（基尔大学理论物理与天体物理研究所）
- Kiel Nano, Surface and Interface Science KiNSIS, Kiel University（基尔大学基尔纳米、表面与界面科学中心）
- Department of Chemistry and Biochemistry, University of California, Santa Barbara（加州大学圣塔芭芭拉分校化学与生物化学系）
- Materials Department, University of California, Santa Barbara（加州大学圣塔芭芭拉分校材料系）
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中文总结 AI 辅助
本文提出非平衡$GW$近似的实时Dyson展开方法，以时间线性成本恢复关联谱，评估多种参考传播子，在驱动晶格模型中验证了其准确性与适用性。
中文摘要 AI 辅助
电子谱为凝聚态系统中的激发和关联提供了直接洞察。它们的描述需要超越平均场的电子关联。在平衡态中，$GW$近似已成为许多材料首选的方法。然而，将该近似扩展到非平衡态具有挑战性。在非平衡格林函数方法框架内，全双时$GW$模拟的计算成本随传播时间至少呈三次方增长，而改进的标度方案如时间局域（绝热）近似或广义Kadanoff-Baym ansatz通常在谱中仅保留平均场特征。最近引入的实时Dyson展开以时间线性成本恢复了谱中的动力学关联，但迄今为止仅限于使用平均场参考传播子的二阶Born近似。在这里，我们针对非平衡$GW$自能公式化并实现了RT-DE，其中参考传播子具有一般形式，其非对角演化是时间局域的。特别地，我们评估了Hartree-Fock传播子、具有非平衡屏蔽的静态屏蔽交换传播子，以及基于Hartree-Fock GKBA的关联传播子。针对具有长程相互作用的驱动双带晶格模型，与精确对角化的基准测试表明，平均场和静态屏蔽参考产生了最准确的谱，包括平均场水平上不存在的卫星结构，而基于GKBA的方法最能捕捉散射诱导的占据数动力学，但人为地展宽和分裂了谱峰。当应用于超出精确方法可达范围的大系统时，该方案解析了价带的激子副本以及被识别为激子shake-up的卫星结构，以及它们随激发密度增加而重塑的过程。
英文摘要
Electronic spectra provide direct insight into the excitations and correlations of condensed matter systems. Their description requires electron correlations beyond mean field. In equilibrium, the $GW$ approximation has become the method of choice for many materials. Extending this approximation to nonequilibrium, however, is challenging. Full two-time $GW$ simulations within the nonequilibrium Green's functions approach scale at least cubically with propagation time, whereas improved scaling schemes such as time-local (adiabatic) approximations or the generalized Kadanoff--Baym ansatz usually retain only mean-field character in the spectra. The recently introduced real-time Dyson expansion recovers dynamical correlations in the spectrum at time-linear cost, but has so far been restricted to the second-order Born approximation with mean-field reference propagators. Here we formulate and implement the RT-DE for the nonequilibrium $GW$ self-energy with reference propagators of general form whose off-diagonal evolution is time local. In particular, we assess Hartree--Fock propagators, propagators with statically screened exchange with nonequilibrium screening, and a correlated propagator based on the Hartree--Fock GKBA. Benchmarks against exact diagonalization for a driven two-band lattice model with long-range interactions show that the mean-field and statically screened references yield the most accurate spectra, including satellite structures absent at mean-field level, whereas the GKBA-based approach best captures scattering-induced occupation dynamics, but artificially broadens and splits spectral peaks. When applied to large systems that are beyond the reach of exact methods, the scheme resolves the excitonic replica of the valence band and satellites identified as exciton shake-up, as well as their reshaping with increasing excitation density.
