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arXiv · 1211.4357

The even-odd effect in short antiferromagnetic Heisenberg chains

A. Machens·N. P. Konstantinidis·O. Waldmann·I. Schneider·S. Eggert
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Abstract

Motivated by recent experiments on chemically synthesized magnetic molecular chains we investigate the lowest lying energy band of short spin-$s$ antiferromagnetic Heisenberg chains focusing on effects of open boundaries. By numerical diagonalization we find that the Landé pattern in the energy levels, i.e. E(S) \propto S(S+1) for total spin S, known from e.g. ring-shaped nanomagnets, can be recovered in odd-membered chains while strong deviations are found for the lowest excitations in chains with an even number of sites. This particular even-odd effect in the short Heisenberg chains cannot be explained by simple effective Hamiltonians and symmetry arguments. We go beyond these approaches, taking into account quantum fluctuations by means of a path integral description and the valence bond basis, but the resulting quantum edge-spin picture which is known to work well for long chains does not agree with the numerical results for short chains and cannot explain the even-odd effect. Instead, by analyzing also the classical chain model, we show that spatial fluctuations dominate the physical behavior in short chains, with length N < exp(πs), for any spin s. Such short chains are found to display a unique behavior, which is not related to the thermodynamic limit and cannot be described well by theories developed for this regime.

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A. Machens, N. P. Konstantinidis, O. Waldmann, I. Schneider, S. Eggert. 2012-11-19. The even-odd effect in short antiferromagnetic Heisenberg chains. https://doi.org/10.1103/physrevb.87.144409

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