Effective Hamiltonian for a Half-filled Asymmetric Ionic Hubbard Chain with Alternating On-site Interaction

TL;DR

This paper derives an effective spin Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interactions, revealing complex spin interactions in the strong repulsion limit.

Contribution

It introduces a novel effective Hamiltonian capturing the complex spin interactions in the asymmetric ionic Hubbard model with alternating on-site interactions.

Findings

Effective Hamiltonian is an anisotropic $XXZ$ Heisenberg chain.

Includes alternating next-nearest-neighbor and three-spin couplings.

Accounts for uniform and staggered magnetic fields.

Abstract

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin $S=1/2$ anisotropic $XXZ$ Heisenberg chain with alternating next-nearest-neighbor and three-spin couplings in the presence of a uniform and a staggered magnetic field.