Based on the effective spin-ladder model, we compute the negativity and geometric quantum discord (GQD) between two edge spins in zigzag graphene nanoribbons (ZGNRs) thermalized with a reservoir at temperature T (canonical ensemble). The results show that the entanglement only exists in antiferromagnetically coupled spin pairs, and completely vanishes between any two spins at the same ribbon edge. Intriguingly, the dominant entanglement always occurs in the nearest inter-edge coupled spin pairs, which is very robust even at room temperature. By contrast, almost all edge spin pairs can hold non-zero GQD, which strongly depends on the ribbon width. To get further insight into the properties of entanglement, the multiparticle entanglement (ME) shared between three spins is studied. The results show that ME always exists among spins located at different edges, and it is more robust than the corresponding two-spin entanglement in against the temperature. These remarkable properties make ZGNRs very promising for possible applications in quantum information processing.
Recent progress in programmable quantum simulators motivates exact benchmarks for nonequilibrium dynamics in topological quantum matter. We study the Kitaev honeycomb model driven through its critical regions by a linear ramp of the bond coupling Jz over a ramp time τ, comparing zigzag and armchair ribbons with fully periodic tubes. The production of excitations exhibits a geometry-dependent finite-size crossover controlled by N2/τ, the ratio of the ribbon width to the Kibble--Zurek length. Periodic tubes obey the expected critical-line Kibble--Zurek scaling and serve as the boundary-free benchmark. Zigzag ribbons follow the same scaling until defect production is exponentially suppressed by a finite-width algebraic gap floor associated with the formation of Majorana edge modes, whose occupation is pinned by inversion parity. Armchair ribbons instead support transient Majorana edge modes with exponentially small gaps, producing width-parity-dependent defect plateaus: exactly one defect per unit length for odd widths and an approximate, transient plateau near one half for even widths. The quench-generated entanglement entropy and fermionic logarithmic negativity inherit the same geometry-dependent structure, and the negativity further distinguishes the coherence-borne entanglement of the Kibble--Zurek regime from the population-borne entanglement of the edge-mode plateaus. These results identify boundary Majorana modes as the mechanism controlling departures from ideal Kibble--Zurek dynamics and provide geometry-resolved benchmarks for programmable simulations of topological matter.
A $\ensuremath{\pi}$-electron network in nanographite systems with zigzag edges exhibits strongly localized edge states, which are expected to have peculiar properties. We study effects of electron-electron interactions on ground-state properties of zigzag nanographite ribbons and open-ended zigzag nanotubes by means of the weak-coupling renormalization group and the density-matrix renormalization-group method. It is shown that the ground state is a spin-singlet Mott insulator with finite charge and spin gaps. We also find that the edge states are robust against the electronic correlations, resulting in edge-effective spins that can flip almost freely. The schematic picture for the low-energy physics of the systems is discussed.