Abstract
The Hubbard Hamiltonian, while not one of the most successful models for π electrons in benzene, has been extensively investigated in the literature. As part of our general study of that model, we have computed all the energy levels for all values of the repulsion parameter—a task that has not been undertaken before. After extracting all the symmetry of the model we found, to our great surprise, many instances of permanent degeneracy of levels with different symmetry and also crossing of levels of the same symmetry. We can also demonstrate that there is no hidden symmetry to account for these effects. Since these results run counter to one of the oldest folk theorems in quantum chemistry, our otherwise uninspiring graphs may be of general interest.
Accorded the Boris Pregel Award for Research in Chemical Physics in 1970 by the New York Academy of Sciences.
This work was partially supported by National Science Foundation Grant GP-9414.
This work was partially supported by Statens Naturvidenskabelige Forskningsraad grant 511-208/69.
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Heilmann, O.J., Liebt, E.H. (2004). Violation of the Noncrossing Rule: The Hubbard Hamiltonian for Benzene. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_2
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