Correlation and confinement induced itinerant ferromagnetism in chain structures

TL;DR

This paper presents an exact theoretical demonstration that electron correlation and confinement in a zig-zag chain structure induce ferromagnetism in a Hubbard model, supporting the idea that Coulomb interactions can stabilize magnetic states in organic systems.

Contribution

It provides an exact many-body ground state solution showing how confinement and correlation lead to ferromagnetism in a non-flat band Hubbard chain.

Findings

Exact ground states demonstrate correlation-induced ferromagnetism.

Operators become connected as carriers increase, leading to spin correlation.

Supports the viability of Coulomb interaction in stabilizing magnetic states in organic materials.

Abstract

Using a positive semidefinite operator technique one deduces exact ground states for a zig-zag hexagon chain described by a non-integrable Hubbard model with on-site repulsion. Flat bands are not present in the bare band structure, and the operators $\hat B^{\dagger}_{\mu,\sigma}$ introducing the electrons into the ground state, are all extended operators and confined in the quasi 1D chain structure of the system. Consequently, increasing the number of carriers, the $\hat B^{\dagger}_{\mu,\sigma}$ operators become connected i.e. touch each other on several lattice sites. Hence the spin projection of the carriers becomes correlated in order to minimize the ground state energy by reducing as much as possible the double occupancy leading to a ferromagnetic ground state. This result demonstrates in exact terms in a many-body frame that the conjecture made at two-particle level by G. Brocks et al. [Phys.Rev.Lett.93,146405,(2004)] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes is clearly viable, and opens new directions in the search for routes in obtaining organic ferromagnetism. Due to the itinerant nature of the obtained ferromagnetic ground state, the systems under discussion may have also direct application possibilities in spintronics.