The theoretical description of strongly correlated fermion systems on a lattice is so non-trivial, that exact solutions are possible only in rare special cases (for simplified models or in special geometries or in certain limits). For example, some one-dimensional models are soluble by the Bethe ansatz.
However, the exact solutions described in the articles cited below are based on other principles. In the first two papers we investigate simplified correlation models, namely the Hubbard model with long-range hopping and the so-called Falicov-Kimball model. The third paper discusses a Hubbard model with the simple geometry of a star, and the fourth clarifies the phase diagram of the Hubbard model in a strong magnetic field near a fully polarized ferromagnetic state.
Exact Solution and Thermodynamics of the Hubbard Model with Infinite-Range Hopping
Peter van Dongen and Dieter Vollhardt
Phys. Rev. B40 7252-7255 (1989)
Exact Mean-Field Hamiltonian for Fermionic Lattice Models in High Dimensions
P. G. J. van Dongen and D. Vollhardt
Phys. Rev. Lett. 65 1663-1666 (1990)
The Hubbard Star
P. G. J. van Dongen, J. A. Vergés and D. Vollhardt
Z. Phys. B84 383-392 (1991)
Mott transition near the ferromagnetic state
P. G. J. van Dongen and V. Janiš
Phys. Rev. Lett. 72 3258-3261 (1994)