Infinite-Dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics

Miki Wadati, Yuko Akutsu

Fabian H. L. Eßler, V. E. Korepin, Kareljan Schoutens

We present a new model describing strongly correlated electrons on a general d-dimensional lattice. It is an extended Hubbard model and it contains the t-J model as a special case. The model naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using an \ensuremath{\eta}-pairing mechanism we can construct eigenstates of the Hamiltonian with off-diagonal long-range order. In the attractive case the exact ground state is superconducting in any number of dimensions. On a one-dimensional lattice, the model is exactly solvable by Bethe ansatz.

Marcelo J. Rozenberg

C. Gruber, D. F. Wang

We review some recent progresses in study of the 1D strongly correlated electron systems of long range hopping and exchange. The systems are completely integrable, with infinite number of constants of motions. The results of the physical properties, such as wavefunctions, the full excitation spectrum and the thermodynamics, are also reviewed.

Dai S. Hirashima, 平島 大

Uwe Grimm, Paul A. Pearce

We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the two-colour braid-monoid algebra describes the Yang-Baxter algebra of the critical dilute A-D-E models which were recently introduced by Warnaar, Nienhuis and Seaton(1992) as well as by Roche(1992). These and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure. It is conjectured that the Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.