We review the approach of generalized permutator to produce a class of
integrable quantum Hamiltonians, as well as the technique of Sutherland species
(SS) to map a subclass of it into solvable spinless fermions models. In
particular, we apply the above scheme to construct integrable interacting
electron Hamiltonians: first we review the extended Hubbard case, discussing
both ground state and thermodynamics; then we pass to constrained fermion
models, generating 56 integrable cases, among which both supersymmetric t-J
model and infinite U Hubbard model are obtained, as well as other physically
interesting cases, such as a particular t-V model. For the latter we describe
how the complete spectrum can be gained by means of SS technique. Finally we
speculate about possible applications to spin S models.Comment: Review article; 12 pages, 4 figures. Appeared on Recent Research
Developements in Physics 5, 513-534 (Transworld Research Network, India,
2004
