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Revisiting the Froehlich-type transformation when degenerate states are present | | M. Acquarone
; C.I.Ventura
; | | Date: |
27 Oct 2006 | | Subject: | Strongly Correlated Electrons; Superconductivity | | Abstract: | We focus on the definition of the unitary transformation leading to an effective second order Hamiltonian, inside degenerate eigensubspaces of the non-perturbed Hamiltonian. We shall prove, by working out in detail the Su-Schrieffer-Heeger Hamiltonian case, that the presence of degenerate states, including fermions and bosons, which might seemingly pose an obstacle towards the determination of such "Froehlich-transformed" Hamiltonian, in fact does not: we explicitly show how degenerate states may be harmlessly included in the treatment, as they contribute with vanishing matrix elements to the effective Hamiltonian matrix. In such a way, one can use without difficulty the eigenvalues of the effective Hamiltonian to describe the renormalized energies of the real excitations in the interacting system. Our argument applies also to few-body systems where one may not invoke the thermodynamic limit to get rid of the "dangerous" perturbation terms. | | Source: | arXiv, cond-mat/0610786 | | Services: | Forum | Review | PDF | Favorites | |
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