The orbital relaxation: a possible origin of t-J model with large J

TL;DR

This paper explores the physical origin of the t-J model in high-temperature superconductivity, showing it can be derived from a Hubbard model with occupation-dependent hopping, especially for large J/t ratios.

Contribution

It demonstrates that a Hubbard model with occupation-dependent hopping reduces to an effective t-J-t' model with no upper J/t bound, explaining the origin of large J/t ratios.

Findings

Exact diagonalization shows equivalence between models for large U and J/t up to 16.

t-U and t-J models only match t-J-t' for small J.

Implications for high-T_C superconductivity are discussed.

Abstract

Whereas the t-J model has gained wide popularity among physicists as a model for high-T_C superconductivity, its physical origin is not at all clear. In this communication we show that the Hubbard model with occupation-dependent hopping (t_1-t_2-t_3-U model), recently proposed to account for the relaxation of doubly-occupied orbitals, reduces, in a physically relevant parameter region, to an effective t-J-t' model with no upper bound on the J/t ratio. Results of exact diagonalization studies on finite size systems demonstrate the equivalence between the t_1-t_2-t_3-U model with intermediate/large U and the t-J-t' model even for very large J/t ratio (up to 16). On the contrary, t-U and t-J models turn out to be equivalent to t-J-t' model only for very small J values (J much smaller than t). Implications of the results on high-T_C superconductivity are briefly discussed.