Diagonalization of the transfer matrix of the free-fermion model. III

B. U. Felderhof

B. U. Felderhof

Vladimir V. Bazhanov, Yu. G. Stroganov

J. Rae

N. Z. Iorgov, O. Lisovyy

We consider the general -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the -symmetric BBS τ (2) -model with n = 2. Translating Kaufman's fermionic approach to diagonalization of Ising-like transfer matrices into the language of Grassmann integrals, we determine the transfer matrix eigenvectors and observe that they coincide with the eigenvectors of a square lattice Ising transfer matrix. This allows us to find exact finite-lattice form factors of spin operators for the statistical model and the associated finite-length quantum chains, of which the most general is equivalent to the XY chain in a transverse field.

Rodolfo Cuerno, A Gonzalez-Ruiz

Diagonal solutions for the reflection matrices associated to the elliptic R matrix of the eight-vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY Hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford-Hopf algebra.