Identification and Optimization of Accurate Spin Models for Open-Shell Carbon Ladders with Matrix Product States

TL;DR

This paper investigates the magnetic properties of non-bipartite carbon nanostructures, mapping their low-energy behavior onto an effective spin model using advanced computational techniques, thus clarifying their correlated magnetic interactions.

Contribution

It introduces an optimized fermionic mode approach to accurately model spin interactions in non-bipartite nanographene ladders, connecting complex electronic structure to simplified spin models.

Findings

Low-energy properties map onto a frustrated J1-J2 Heisenberg chain.

Effective spin interactions are well described by the optimized modes.

The approach clarifies the emergence of spin degrees of freedom in nanographene.

Abstract

Open-shell nanographenes offer a controlled setting to study correlated magnetism emerging from $\pi$-electron systems. We analyze oligo(indenoindene) molecules, non-bipartite carbon ladders whose tight-binding spectra feature a gapped, weakly dispersing manifold of quasi-zero modes, and show that their low-energy properties can be effectively mapped onto an interacting set of spin-1/2 degrees of freedom. Using Density Matrix Renormalization Group simulations of the full Fermi-Hubbard model, we obtain their excitation spectra, entanglement profiles, and spin-spin correlations. We then construct optimized delocalized fermionic modes that act as emergent spins and show that their interactions are well described by a frustrated $J_1$-$J_2$ Heisenberg chain. This effective description clarifies how spin degrees of freedom arise and interact in non-bipartite nanographene ladders, providing a compact and accurate representation of their correlated behavior.