Direct Exchange versus the indirect Exchange of the t-J Hamiltonian in HTSC Cuprates

Abstract

The direct exchange integral and the transfer integral are calculated for the anti-bonding wave-function of the HTSC cuprates. The direct exchange integral yields a value three times larger than the indirect exchange of the t-J Hamiltonian. It also predicts positive exchange energy for neighboring parallel spins, contrary to the prediction of zero energy by the t-J Hamiltonian. A modified t-J Hamiltonian is proposed, and the implications of the results are discussed.

This paper has been withdrawn due to some errors. The main error is the wrong spin function of Eq. (5), which makes equations (13) and (14) incorrect, and in turn puts doubts on the final conclusions