Finite-lattice form factors in free-fermion models

Abstract

We consider the general ${\mathbb{Z}}_2$-symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and ${\mathbb{Z}}_n$-symmetric BBS ${\tau }^{(2)}$-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 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.

12 pages; v2: minor changes, added refs; to appear in J. Stat. Mech

References in corpus (3)

• Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elements
• Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite lattice
• Ising correlations and elliptic determinants

Cited by in corpus (1)

• Effective free-fermionic form factors and the XY spin chain