Quantum magnetism of topologically-designed graphene nanoribbons

TL;DR

This study uses numerical simulations to investigate the quantum magnetism of topologically-designed graphene nanoribbons, finding they are nonmagnetic at realistic interaction strengths, aligning with experimental observations.

Contribution

It provides the first detailed numerical analysis of the magnetic properties of topologically-designed GNRs using Hubbard models and advanced simulation techniques.

Findings

Two-band Hubbard chain is nonmagnetic, contrasting mean-field predictions.

Magnetic order develops only at large interactions, beyond realistic values.

Experimentally relevant GNRs are nonmagnetic, consistent with observations.

Abstract

Based on the Hubbard models, quantum magnetism of topologically-designed graphene nanoribbons (GNRs) is studied using exact numerical simulations. We first study a two-band Hubbard model describing the low-energy topological bands using density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) methods. It is found the spin correlations decay quickly with the distance, and the local moment is extrapolated to zero in the presence of symmetry-breaking terms. The results show that the two-band Hubbard chain is nonmagnetic, which is in contrast to the mean-field calculation predicting a critical interaction for the magnetic transition. We then include the Hubbard interaction to the topological-designed GNRs. For large interactions, the spin correlations keep finite for all distances, and the magnetic order develops. The local moment is extrapolated to almost zero for weak interactions, and begins to increase rapidly from a critical interaction. The estimated critical value is much larger than the realistic value in graphene, and we conclude the experimentally relevant GNRs is nonmagnetic, which is consistent with the experimental results.