Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation

TL;DR

This paper compares mean-field theory, exact diagonalization, and quantum Monte Carlo simulations to study the magnetic properties of finite graphene samples, finding good agreement under moderate Coulomb interactions.

Contribution

It evaluates the accuracy of mean-field theory against more exact methods for predicting magnetism in finite graphene structures.

Findings

Good quantitative agreement between methods for moderate Coulomb interactions

Mean-field theory reliably predicts ferromagnetic edge states in graphene

Accuracy diminishes with very strong Coulomb interactions

Abstract

The magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zig-zag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.