Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

Understand

We apply our new approach of quantum Separation of Variables (SoV) to the complete characterization of the transfer matrix spectrum of quantum integrable lattice models associated to gl(n)-invariant R-matrices in the fundamental representations.

• We consider lattices with N sites and quasi-periodic boundary conditions associated to an arbitrary twist K having simple spectrum (but not necessarily diagonalizable).
• In our approach the SoV basis is constructed in an universal manner starting from the direct use of the conserved charges of the models, i.e., from the commuting family of transfer matrices.
• Using the integrable structure of the models, incarnated in the hierarchy of transfer matrices fusion relations, we prove that our SoV basis indeed separates the spectrum of the corresponding transfer matrices.