Variationnal study of ferromagnetism in the t1-t2 Hubbard chain

TL;DR

This study investigates ferromagnetism in a one-dimensional Hubbard model with next-nearest neighbor hopping, identifying conditions under which saturated ferromagnetism is excluded and analyzing the critical interaction strength across different densities.

Contribution

The paper introduces a variational approach to analyze ferromagnetism in the Hubbard chain with next-nearest neighbor hopping, revealing the behavior of the critical interaction strength.

Findings

Saturated ferromagnetism is excluded for U < U_c.

Critical interaction U_c(n) has a minimum at a specific density n_c.

U_c(n) diverges as the density approaches 1.

Abstract

A one-dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping is studied variationally. This allows to exclude saturated ferromagnetism for $U < U_c$. The variational boundary $U_c (n)$ has a minimum at a ``critical density'' $n_c$ and diverges for $n \rightarrow 1$.