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.

arXiv comment12 pages; v2: minor changes, added refs; to appear in J. Stat. Mech

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• Front dynamics in the XY chain after local excitations
• Effective free-fermionic form factors and the XY spin chain
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Form-factors of the finite quantum XY-chain
• Form factors of twist fields in the lattice Dirac theory