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Fluxes and Dimers in the Hubbard Model

In: Proceedings of the International Congress of Mathematicians

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  • Elliott H. Lieb

    (Princeton University, Departments of Mathematics and Physics)

Abstract

The Hubbard model is the simplest conceivable example of interacting quantum- mechanical particles — yet it seems to have real world applications. Like the Ising model, it is “merely” a discrete lattice model, but despite four decades of research it is far from being understood rigorously; or even heuristically in many respects. The most amenable and symmetric situation is the “half-filled band”, in which the number of particles equals the number of vertices in the lattice. Two conjectures about the model at half-filling have very recently been proved and are discussed here. The first can be found in [LN] and the second in [LE].

Suggested Citation

  • Elliott H. Lieb, 1995. "Fluxes and Dimers in the Hubbard Model," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 1279-1280, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_122
    DOI: 10.1007/978-3-0348-9078-6_122
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