Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov $τ_2$-model for N=2

Abstract

We find a representation of the row-to-row transfer matrix of the Baxter-Bazhanov-Stroganov $τ_2$-model for N=2 in terms of an integral over two commuting sets of grassmann variables. Using this representation, we explicitly calculate transfer matrix eigenvectors and normalize them. It is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain Toeplitz matrices.