Electron-phonon coupling in the self-consistent Born approximation of the t-J model

O. Gunnarsson; O. Rösch

doi:10.1103/physrevb.73.174521

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Electron-phonon coupling in the self-consistent Born approximation of the t-J model

O. Gunnarsson·O. Rösch

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Abstract

We study an undoped t-J model with electron-phonon interaction using the self-consistent Born approximation (SCBA). By neglecting vertex corrections, the SCBA solves a boson-holon model, where a holon couples to phonons and magnons. Comparison with exact diagonalization results for the t-J model suggests that the SCBA describes the electron-phonon interaction fairly accurately over a substantial range of J/t values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small J/t and due to the replacement of the t-J model by the boson-holon model for large J/t. For typical values of J/t, the electron-phonon part Sigma_ep of the electron self-energy has comparable contributions from the second order diagram in the electron-phonon interaction and a phonon induced change of magnon diagrams. A very simple approximation to Sigma_ep gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.

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O. Gunnarsson, O. Rösch. 2006-02-14. Electron-phonon coupling in the self-consistent Born approximation of the t-J model. https://doi.org/10.1103/physrevb.73.174521

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