From the double-exchange Hamiltonian to the $t-J$ model: Classical spins

TL;DR

This paper derives the $t-J$ model with classical localized spins starting from the double-exchange Hamiltonian under strong Hund exchange coupling, providing a theoretical link between these models.

Contribution

It introduces a derivation of the $t-J$ model from the double-exchange Hamiltonian specifically with classical spins, clarifying their relationship.

Findings

Established the $t-J$ model as an effective limit of the double-exchange Hamiltonian.

Demonstrated the conditions under which the derivation holds.

Provided insights into the role of classical spins in the $t-J$ framework.

Abstract

From the double-exchange Hamiltonian with classical localized spins in the limit of large but finit Hund exchange coupling we obtain the $t-J$ model (with classical localized spins).