Simplified diagrammatic expansion for effective operator

Details Simplified diagrammatic expansion for effective operator Simplified diagrammatic expansion for effective operator

2005-05-24

arxiv.org/abs/quant-ph/0505179v1

J. Chem. Phys., Vol. 121, No. 11, 5071-5076 (15 September 2004)

Physics

Quantum Physics

5 journal pages, 4 figures

Scientific paper

10.1063/1.1782071

For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity.

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