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On Adiabatic and Non‐Adiabatic Improvements of the Mean‐Field Approximation for Fermion‐ or (Pseudo‐)Spin‐Boson Interaction
Author(s) -
Enders P.
Publication year - 1986
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19864980607
Subject(s) - physics , hamiltonian (control theory) , boson , quantum mechanics , fermion , bogoliubov transformation , mean field theory , adiabatic process , ground state , fock space , quantum electrodynamics , mathematics , mathematical optimization
Starting at the tight‐binding electron‐phonon Hamiltonian for a linear diatomic chain (half‐filled Peierls chain with extrinsic gap), being a special realization of the fermion‐ or (pseudo)spin‐boson interaction, we examine some improvements of the usual MFA: an improved phonon trial function with (anti‐)symmetrized coherent states; a generalized Hartree‐Fock decoupling with anomalous averages after transforming the electron‐phonon interaction to an effective electron‐electron one; a pure bosonic treatment using the Holstein‐Primakoff transformation. Systematic improvements at the ground state are obtained. But for finite temperatures the formalism soon becomes quite elaborate. Nevertheless, these different approaches provide valuable insights into various aspects of this interaction problem. Furthermore, the unifying features of various particle‐particle interactions are emphasized and the connection between solid‐state (physics) and (molecular) quantum chemistry is mentioned.