Abstract
Molecular wires of the acene-family can be viewed as a physical realization of a two-rung ladder Hamiltonian. For acene-ladders, closed-shell ab initio calculations and elementary zone-folding arguments predict incommensurate gap oscillations as a function of the number of repetitive ring units, NR, exhibiting a period of about ten rings. Results employing open-shell calculations and a mean-field treatment of interactions suggest anti-ferromagnetic correlations that could potentially open a large gap and wash out the gap oscillations. Within the framework of a Hubbard model with repulsive on-site interaction, U, we employ a Hartree-Fock analysis and the density matrix renormalization group to investigate the interplay of gap oscillations and interactions. We confirm the persistence of incommensurate oscillations in acene-type ladder systems for a significant fraction of parameter space spanned by U and NR.
Highlights
The question how properties of a macroscopic system emerge when more and more atoms or molecules accumulate exhibits many different facets and, for that reason, reappears every once in a while in different contexts
A conceptually analogous situation arises in mesoscopic physics: when a quantum dot couples to an electrode, the dot states hybridize with contact states, thereby acquiring the level broadenings, Γ, that signal finite lifetime effects
For non-interacting systems, the optical gap corresponds to the gap between the highest occupied molecular orbital (HoMO) and the lowest unoccupied molecular orbital (LuMO), as it is given by the lowest particle-hole excitation
Summary
The question how properties of a macroscopic system emerge when more and more atoms or molecules accumulate exhibits many different facets and, for that reason, reappears every once in a while in different contexts. In the long-wire limit, quantum fluctuations tend to destabilize mean-field ordered phases that break a continuous symmetry.18 In this (quantum-disordered) phase, the order-parameter exhibits significant short-range correlations that leave a characteristic signature in local probe measurements. We clarify the fate of the anti-ferromagnetic correlations in acene-type ladders in the presence of quantum fluctuations, i.e., by providing a joint analysis from the Hartree-Fock (HF) mean field and density matrix renormalization group (DMRG). By microscopic DMRG analysis, we show that in short ladders quantum fluctuations destroy the long-range order They significantly reduce the HF excitation gap, restoring the IO signature and up to intermediate interaction strengths of the order of the bandwidth
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