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

TL;DR

This paper investigates electron-phonon interactions in the undoped t-J model using the self-consistent Born approximation, revealing how phonons influence polaron formation and effective mass with good accuracy compared to exact methods.

Contribution

It applies the SCBA to the t-J model with electron-phonon coupling, providing insights into polaron formation and the relative strength of magnon and phonon interactions.

Findings

SCBA describes electron-phonon interactions well over a range of J/t.

Phonons can induce small polaron formation despite weaker nominal coupling.

Magnons have a stronger nominal coupling but phonons dominate polaron effects.

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.