Parity law of the singlet-triplet gap in graphitic ribbons

TL;DR

This paper investigates whether the parity law of the singlet-triplet gap observed in square ladders applies to graphitic ribbons, demonstrating that ribbons with odd width are gapped while even width ribbons are gapless.

Contribution

It extends the parity law of the singlet-triplet gap from square ladders to fused polyacenic systems like graphite ribbons, supported by numerical calculations.

Findings

Ribbons with odd number of benzene rings are gapped.

Ribbons with even number of benzene rings are gapless.

Numerical methods confirm the parity law in these systems.

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 $n\_{\omega}$ 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 $n\_{\omega}$.