Bethe Ansatz and Coordinate Bethe Ansatz, application to three state Hamiltonians
by
Luc Frappat
→
Europe/Rome
248 (Building C, first floor)
248
Building C, first floor
Description
Quantum integrable systems have a long history. Originally, solving
such models was done through the Coordinate Bethe Ansatz, while the
underlying mathematical structure was not manifest. In the eighties,
the R-matrices, solutions of the celebrated Yang-Baxter equation, has
become a cornerstone of the resolution of such systems. R-matrices
contain the Hamiltonian of the system and constitute the basic
ingredient of the Algebraic Bethe Ansatz that provides the eigenvalues
and eigenfunctions of the model. After presenting and comparing the
two ansatz, we review some of the strategies that can be implemented
to infer an R-matrix from the knowledge of its Hamiltonian, and apply
this framework to the case of three-state Hamiltonians with rank 1
symmetry and nearest-neighbour interactions in the context of spin
chains.
