We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent Dyson expansions and solving the resulting set of equations. This method, dubbed the variational approximation, is both very dependable and flexible, since it is a systematic expansion with precise control over elementary physical processes. It allows for deep insight into the underlying physics of polaron formation as well as for inclusion of many physical constraints, such as excluding crossing diagrams and double occupation constraint, which are not included in the Self-Consistent Born Approximation. Here we examine the role and importance of such constraints by analyzing various spectral functions obtained in second order VA.
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…
Green's Function-Free Formalism of Projective Truncation Approximation
International Center for Quantum Materials and School of Physics, Peking University（北京大学量子材料中心及物理学院）；School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院及量子态构建与操控教育部重点实验室）
Unifying Variational and Dynamical Quantum Embedding: From Ghost Gutzwiller Approximation to Dynamical Mean-Field Theory
Center for Computational Quantum Physics, Flatiron Institute（平顶山研究所计算量子物理中心）；Department of Physics, National Chung Cheng University（国立中正大学物理系）；Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文学系）；Physics and Astronomy Department, Rutgers University（罗格斯大学物理与天文学系）；Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory（布鲁克海文国家实验室凝聚态物理与材料科学系）；Physics Department, Boston University（波士顿大学物理系）；Université Paris-Saclay, CNRS, CEA, Institut de physique théorique（巴黎萨克雷大学、法国国家科学研究中心、法国原子能和替代能源委员会、理论物理研究所）；School of Physics and Astronomy, Rochester Institute of Technology（罗切斯特理工学院物理与天文学院）
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…
