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arXiv · 1102.2145

Finite-lattice form factors in free-fermion models

N. Iorgov·O. Lisovyy
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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 $τ^{(2)}$-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 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.

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N. Iorgov, O. Lisovyy. 2011-03-24. Finite-lattice form factors in free-fermion models. https://doi.org/10.1088/1742-5468%2F2011%2F04%2Fp04011

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