Eur. Phys. J. B 51, 517-522 (2006)
https://doi.org/10.1140/epjb/e2006-00259-9

Parity law of the singlet-triplet gap in graphitic ribbons

¹ Laboratoire de Chimie et Physique Quantique, IRSAMC/UMR5626, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
² Laboratoire de Physique Théorique, IRSAMC/UMR5152, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
³ CRISMAT, 6 Bd Maréchal Juin, 14050 Caen Cedex, France
⁴ Department of Applied Physics, University of Tokyo, Tokyo, 113-8656, Japan

Corresponding author: ^a sylvain.capponi@irsamc.ups-tlse.fr

Received: 24 January 2006
Revised: 14 March 2006
Published online: 28 June 2006

Abstract

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_ω 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) confirms the parity law and the gapless character of the ribbon for even n_ω.