Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

TL;DR

This paper investigates quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons using quantum Monte Carlo simulations, revealing a quantum critical point separating disordered and magnetic phases.

Contribution

It demonstrates the existence of a quantum phase transition in effective spin models for graphene nanoribbons, accounting for long-range intra-edge couplings and quantum fluctuations beyond mean-field theory.

Findings

Identifies a quantum critical point at finite inter-edge coupling.

Shows a transition from a quantum disordered to a gapless magnetic phase.

Relates the effective spin model to coupled Haldane-Shastry chains.

Abstract

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.