Related papers: Combinatorial Mori-Zwanzig Theory
We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation green's functions in the non-relativistic case. These non-linear and coupled equations of motion…
We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix…
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by…
We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional…
We give a precise connection between combinatorial Dyson-Schwinger equations and log-expansions for Green's functions in quantum field theory. The latter are triangular power series in the coupling constant $\alpha$ and a logarithmic energy…
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled…
We extend the Nakajima-Zwanzig projection operator technique to the determination of multitime correlation functions of open quantum systems. The correlation functions are expressed in terms of certain multitime homogeneous and…
The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including fluid…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
We present a new method to approximate the Mori-Zwanzig (MZ) memory integral in generalized Langevin equations (GLEs) describing the evolution of smooth observables in high-dimensional nonlinear systems with local interactions. Building…
We present the concept, derivation, and implementation of dynamical configuration interaction, a quantum embedding theory that combines Green's function methodology with the many-body wave function. In a strongly-correlated active space, we…
Precise algorithms capable of providing controlled solutions in the presence of strong interactions are transforming the landscape of quantum many-body physics. Particularly exciting breakthroughs are enabling the computation of non-zero…
Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods employ exponential wavefunction…
A ``forward walking'' Quantum Monte Carlo (QMC) algorithm has been developed to calculate correlation functions for the Hamiltonian lattice formulation of U(1) Yang-Mills theory in (2+1) dimensions. It is shown that Wilson loops can be…
I review the way the many-body Green functions are used to renormalize the perturbation theory of correlated fermions. The Green functions are introduced to implement systematically dynamical corrections to the static mean-field theory. The…
The GW approximation is a cornerstone of many-body perturbation theory for computing single-particle excitations, yet it fundamentally breaks down in strongly correlated systems where the single-reference picture fails. To overcome this…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building…
We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green's functions-- in closed many-body quantum systems. We show that in a large class of…
Using a general-order ab initio many-body Green's function method, we numerically illustrate several pathological behaviors of the Feynman-Dyson diagrammatic perturbation expansion of one-particle many-body Green's functions as electron…