Quasiparticle Fock-space coupled-cluster theory

Abstract

The quasiparticle Fock-space coupled-cluster (QFSCC) theory, introduced by us in 1985, is described. This is a theory of many-electron systems which uses the second-quantisation formalism based on the algebraic approximation: one chooses a finite spin-orbital basis, and builds a fermionic Fock space to represent all possible antisymmetric electronic states of a given system. The algebraic machinery is provided by the algebra of linear operators acting in the Fock space, generated by the fermion (creation and annihilation) operators. The Fock-space Hamiltonian operator then determines the system's stationary states and their energies. Within the QFSCC theory, the Fock space and its operator algebra are subject to a unitary transformation which effectively changes electrons into some fermionic quasiparticles. A generalisation of the coupled-cluster method is achieved by enforcing the principle of quasiparticle-number conservation. The emerging quasiparticle model of many-electron systems offers useful physical insights and computational effectiveness. The QFSCC theory requires a substantial reformulation of the traditional second-quantisation language, by making full use of the algebraic properties of the Fock space and its operator algebra. In particular, the role of operators not conserving the number of electrons (or quasiparticles) is identified.

Keywords:

• many-electron systems
• fermions
• quasiparticles
• Fock space
• coupled-cluster method

Acknowledgement

One of the authors (LS) wishes to thank the faculty, visitors, and postdocs of the Quantum Theory Project in the years 1983–1990, for providing such a friendly and stimulating scientific environment for the QFSCC project.