Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number $n_{\omega}$ of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin $1/2$ chains, renormalized excitonic treatments and Quantum Monte Carlo) confirm the parity law and the gapless character of the ribbon for even $n_{\omega}$.