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Can Majorana Fermions correctly describe the ordered state of an antiferromagnetic Heisenberg chain?

D. Foerster
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Abstract

To check the reliability of the Majorana representation of quantum spin systems, we use it to compute the ground state energy of an antiferromagnetic spin 1/2 chain to one loop order. We find a very small one loop correction of the mean field energy and a discrepancy of >100% compared to the Bethe Ansatz result. We conclude that a careful handling of the gauge degrees of freedom of this representation is crucial to get correct results.

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D. Foerster. 1997-01-14. Can Majorana Fermions correctly describe the ordered state of an antiferromagnetic Heisenberg chain?. https://arxiv.org/abs/cond-mat/9701093

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