In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals $ψ$ 's are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through $ψ$ 's in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals $ψ$'s are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through $ψ$'s in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.

arXiv:cond-mat/9706033Jun 4, 19971 citation

ASPECTS OF MANY-BODY PERTURBATION THEORY

WORLD SCIENTIFIC eBooksFeb 19, 20190 citations

The electron propagator for non-interacting particles: An alternative approach to quasi-degenerate perturbation theory (QDPT)

J. Schirmer

This article presents an alternative formulation of quasi-degenerate perturbation theory (QDPT). The development results by simplifying established many-body (MB) techniques to systems of non-interacting particles (NIP). While the physical information of a NIP system is fully equivalent with that of the underlying one-particle system, NIP adaptions of MB schemes can acquire useful new roles in the one-particle context. In particular, the algebraic-diagrammatic construction (ADC) approach to the particle-detachment part of the electron propagator, turns into a new formalism of QDPT for the original one-particle system, establishing a diagrammatic perturbation theory for the matrix elements of the effective hamiltonian and the associated effective eigenvector coefficients (EEC). Using the NIP-ADC procedure explicit QDPT expansions are derived through third order. Alternatively, the intermediate state representation (ISR), underlying the ADC approach, allows one to construct the effective secular quantities directly from successive orders in the PT expansions of the NIP ground state and ground-state energy. Moreover, exact closed-form expressions can be derived for the effective hamiltonian and the EEC matrix in terms of 'target state' eigenvectors and eigenvalues of the one-particle system. These results are fully consistent with corresponding expressions derived within the QDPT context. The NIP approach to QDPT is not confined to actual particles but applies to arbitrary quantum systems. Any quantum system can be seen as formally constituting a "hyper-particle" giving rise to a system of non-interacting hyper-particles. The NIP adaptions of the biorthogonal coupled-cluster (BCC) and unitary coupled-cluster (UCC) methods are briefly discussed as well.This article presents an alternative formulation of quasi-degenerate perturbation theory (QDPT). The development results by simplifying established many-body (MB) techniques to systems of non-interacting particles (NIP). While the physical information of a NIP system is fully equivalent with that of the underlying one-particle system, NIP adaptions of MB schemes can acquire useful new roles in the one-particle context. In particular, the algebraic-diagrammatic construction (ADC) approach to the particle-detachment part of the electron propagator, turns into a new formalism of QDPT for the original one-particle system, establishing a diagrammatic perturbation theory for the matrix elements of the effective hamiltonian and the associated effective eigenvector coefficients (EEC). Using the NIP-ADC procedure explicit QDPT expansions are derived through third order. Alternatively, the intermediate state representation (ISR), underlying the ADC approach, allows one to construct the effective secular quantities directly from successive orders in the PT expansions of the NIP ground state and ground-state energy. Moreover, exact closed-form expressions can be derived for the effective hamiltonian and the EEC matrix in terms of 'target state' eigenvectors and eigenvalues of the one-particle system. These results are fully consistent with corresponding expressions derived within the QDPT context. The NIP approach to QDPT is not confined to actual particles but applies to arbitrary quantum systems. Any quantum system can be seen as formally constituting a "hyper-particle" giving rise to a system of non-interacting hyper-particles. The NIP adaptions of the biorthogonal coupled-cluster (BCC) and unitary coupled-cluster (UCC) methods are briefly discussed as well.

arXiv:2309.15721Sep 27, 20230 citations

Perturbation theory of large quantum systems

Nicolaas Marinus Hugenholtz

PhysicaJan 1, 1957463 citations

In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals

ψ

's are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through

ψ

's in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.