本文导出了简并系统多体物理中演化算符的严格非微扰绝热近似。这种近似是用来解决长期存在的问题的初始状态的选择H0导致本征态的H0+V的退化系统。这些初始状态是P0 V P0的本征态，其中P0是H0的简并本征空间上的投影。利用这个结果给出了简并系统的格林函数、统计格林函数和非平衡格林函数的正确定义。这些格林函数的收敛性。
英文摘要：
A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0 V P0, where P0 is the projection onto a degenerate eigenspace of H0. This result is used to give the proper definition of the Green function, the statistical Green function and the non-equilibrium Green function of degenerate systems. The convergence of these Green functions is established.
Fundamental limitations of single-particle Green's-function zeroes as probes of many-body topology
Institut de Physique Théorique, Université Paris Saclay, CEA CNRS（巴黎萨克雷大学理论物理研究所）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）
Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
本课堂讲稿回顾了最近提出的基于格林函数数据压缩的有效从头计算多体计算的稀疏建模方法。稀疏建模技术是基于一个紧凑的正交基，一个中间表示（IR）的基础上，时间和松原格林函数。基于IR基的稀疏采样方法可以有效地求解图解方程。我们描述了IR基的基本性质，稀疏采样方法及其在基于GW近似和Migdal-Eliashberg理论的从头计算中的应用。我们还描述了一个数值库的IR基础和稀疏采样方法，稀疏IR，并提供其示例代码。这份课堂讲稿是在日文评论文章的基础上做了重大修改[H. Shinaoka等人，Solid State Physics 56（6），301（2021）]。
Protocols for a many-body phase microscope: From coherences and d-wave superconductivity to Green's functions
TU Dortmund University（多特蒙德工业大学）；Kyoto University（京都大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the one hand and theories based on many-body wave functions on the other. This link can be used to explicitly construct approximations for the density-matrix functional that are equivalent to standard diagrammatic re-summation techniques and to non-perturbative dynamical mean- field theory in particular. Contrary to functionals of the Green's-function, the exact …
Training biases in machine learning for the analytic continuation of quantum many-body Green's functions
我们解决的问题解析连续的频率格林函数，这是至关重要的多体物理，使用机器学习的基础上的多级残差神经网络。我们专门解决潜在的偏见，可以引入由于使用人工创建的频谱函数，用于训练神经网络。我们还基于Monte Carlo dropout实现了预测谱函数的不确定性估计，这允许识别预测可能不准确的频率区域，并且我们研究了噪声的影响，特别是对于训练期间的噪声水平与实际数据不同的情况。我们的分析表明，这种方法确实可以实现高质量的预测，与广泛使用的最大熵方法相当或更好，但目前由于缺乏可用于训练的真实数据，进一步的改进受到限制。我们还基准我们的方法，通过将其应用到SrVO $_3$的情况下，其中一个准确的谱函数已获得从动态平均场论使用求解器，直接在实际频率轴上工作。
Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons
磁性材料中局域自旋的算符在晶格的不同位置上对易，在同一位置上反对易，因此它们既不是费米子算符，也不是玻色子算符。因此，为了构造图解多体微扰理论，自旋算符通常被映射到玻色子算符，其中Holstein-Primakoff（HP）变换是磁电子学和自旋电子学文献中最广泛使用的变换。然而，为了使计算易于处理，HP变换中的算子的平方根被扩展成截断到某个低阶的泰勒级数。这就对截断HP变换在描述局域自旋相互作用或与传导电子自旋相互作用的非平衡动力学时的有效性范围提出了问题。在这里，我们将精确对角化技术应用于费米子的哈密顿量（即，电子）与HP玻色子相互作用与费米子与原始局域自旋算符相互作用的哈密顿量，以比较它们的多体状态和单粒子平衡或非平衡格林函数。在截断的HP变换中，如果不保留大量的项，费米子与HP玻色子相互作用的哈密顿量将给出不正确的基态和电子谱函数。此外，跟踪非平衡动力学的本地化的自旋在较长的时间间隔，需要越来越多的条款截断HP变换。最后，我们证明了最近提出的[M. Vogl等人，Phys. Rev. Research 2，043243（2020）; J. König等人，10，007（2021）]图解的HP变换解决了截断HP变换的麻烦，同时允许我们导出由有限和固定数量的玻色子-玻色子和电子-玻色子相互作用项组成的精确（明显的厄米特）哈密顿量。
Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $Ω[\mathbf{G}]$ regarded as variational functional of the Green's function $G$ based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger-Ward form. By restricting the input Green's function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To es…
Total energies from variational functionals of the Green function and the renormalized four-point vertex
We derive variational expressions for the grand potential or action in terms of the many-body Green function $G$ which describes the propagation of particles and the renormalized four-point vertex $Γ$ which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the $Ξ$ -functional which plays a role analogously to the usual $Φ$ -functional studied by Baym (G.Baym, Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in many-body systems. We show that any $Ξ$ -derivable theory is also $Φ$ -derivab…
Quasi-Nambu-Goldstone modes in many-body scar models
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences（中国科学院理论科学卡弗里研究所）
