Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid

TL;DR

This paper reveals that in the edge ferromagnetic state of graphene, spin excitations form a continuum due to deconfined spinons, indicating a ferromagnetic Luttinger liquid rather than conventional magnons.

Contribution

It demonstrates the existence of a ferromagnetic Luttinger liquid in graphene's edge states through numerical analysis, highlighting fractionalized spin excitations.

Findings

Absence of well-defined magnons in the edge ferromagnetic state.

Presence of a spinon continuum indicating fractionalized excitations.

Identification of a ferromagnetic Luttinger liquid in graphene edges.

Abstract

The elementary excitations from the conventional magnetic ordered states, such as ferromagnets and antiferromagnets, are magnons. Here, we elaborate a case where the well-defined magnons are absent completely and the spin excitation spectra exhibit an entire continuum in the itinerant edge ferromagnetic state of graphene arising from the flatband edge electronic states. Based on the further studies of the entanglement entropy and finite-size analysis, we show that the continuum other than the Stoner part results from the spin-1/2 spinons deconfined from magnons. The spinon continuum in a magnetically ordered state is ascribed to a ferromagnetic Luttinger liquid in this edge ferromagnet. The investigation is carried out by using the numerical exact diagonalization method with a projection of the interacting Hamiltonian onto the flat band.