Integrable SU(N) vertex models with general toroidal boundary conditions Original Research Article

We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge transformations on the Boltzmann weights in the manner of Baxter [R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982]. The structure of the transfer matrix eigenvectors consists of multi-particle states over such pseudovacuums and the corresponding eigenvalues depend crucially on the boundary matrix eigenvalues. We also discuss for N=2 the peculiar case of twisted boundaries associated to singular matrices.