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Finite-lattice form factors in free-fermion models

Abstract : We consider the general {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 the {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 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.
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Contributor : Oleg Lisovyy <>
Submitted on : Friday, February 1, 2013 - 11:57:29 PM
Last modification on : Monday, December 16, 2019 - 4:02:14 PM

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N. Iorgov, O. Lisovyy. Finite-lattice form factors in free-fermion models. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2011, 04, pp.011. ⟨10.1088/1742-5468/2011/04/P04011⟩. ⟨hal-00783919⟩



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