Hubbard model on hypercubes

We present some exact results for the Hubbard model on d-dimensional hyperc ubes and fillings corresponding to (N-up arrow(down arrow) = N, N-down arro w(up arrow) = 1) with N arbitrary. Introducing a spin formalism associated with the symmetry operations of the hypercube it is shown that the Hubbard model can be rewritten as a spin Hamiltonian defined on a dx(N + I) rectang ular spin lattice. For the two-electron case (N = 1) a logarithmic reductio n of the active part of the Hilbert space can be achieved. It is shown that a very important size reduction can also be achieved for N > I. (C) 1999 E lsevier Science B.V. All rights reserved.