Effective Hamiltonian for a Half-filled Hubbard Chain with Alternating On-site Interactions

TL;DR

This paper derives an effective spin Hamiltonian for a half-filled one-dimensional Hubbard chain with alternating on-site interactions, revealing an asymmetric next-nearest-neighbor exchange in the resulting spin model.

Contribution

It introduces a new effective Hamiltonian capturing the effects of alternating on-site interactions in the Hubbard model, highlighting asymmetric nnn exchange.

Findings

Effective Hamiltonian is a spin 1/2 Heisenberg chain.

Includes asymmetric next-nearest-neighbor exchange.

Applicable in the strong on-site repulsion limit.

Abstract

We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin $S=1/2$ Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.