In this work we propose an algorithm to find critical points of the inner product between an element of the Grassmannian and a fixed point of the projective space of the exterior algebra where the Grassmannian is embedded. This has interesting applications to electronic structure theory, where the wave functions are represented by elements of the exterior algebra. This method is exemplified for a Grassmannian that is a model for the hydrogen molecule, H 2 .

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Soluble models on the triangular and other lattices

R. J. Baxter

Annals of the Israel Physical SocietyJan 1, 19782 citations

Physica A Statistical Mechanics and its Applications

Some results for Grassmannian models on a lattice

Yves Brihaye, Piotr Kosiński

Published Aug 1, 1988• 0 citations

Publisher

DOI: 10.1016/0378-4371(88)90023-4

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We consider the standard quantum logic

{\mathcal L}(H)

associated to a complex Hilbert space

H

, i.e. the lattice of closed subspaces of

H

together with the orthogonal complementation. The orthogonality and compatibility relations are defined for any logic. In the standard quantum logic, they have a simple interpretation in terms of operator theory. For example, two closed subspaces (propositions in the logic

{\mathcal L}(H)

) are compatible if and only if the projections on these subspaces commute. We present both classical and more resent results on transformations of

{\mathcal L}(H)

and the associated Grassmannians which preserve the orthogonality or compatibility relation. The first result in this direction was classical Wigner's theorem.