Low density ferromagnetism in Extended Hubbard ( t-t'-U ) Model

TL;DR

This paper investigates ferromagnetism in a one-dimensional extended Hubbard model with next-nearest neighbor hopping, revealing conditions under which ferromagnetism emerges due to modifications in the density of states.

Contribution

It introduces a self-consistent approach using Hubbard I approximation to map out ferromagnetic phases influenced by next-nearest neighbor hopping in the extended Hubbard model.

Findings

Ferromagnetism exists over a wide range of t' when U is large.

Maximum ferromagnetic density peaks around t'/t ≈ -0.53.

t' modifies the density of states, facilitating ferromagnetism.

Abstract

We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for $<n_\sigma>$, the particle density with spin $\sigma$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor hopping element t' when on-site interaction U is large. The phase diagram as a function of t'/t and the electron density $<n>$ has been obtained by numerically solving the self consistent equation. It is found that the maximum density at which ferromagnetism can occur, peaks around $t'/t \approx -0.53$. We show that this phenomenon is a result of the peculiar way in which the t' term modifies the density of states.