Finite-lattice form factors in free-fermion models

Details Finite-lattice form factors in free-fermion models Finite-lattice form factors in free-fermion models

2011-02-10

arxiv.org/abs/1102.2145v2

J. Stat. Mech. (2011) P04011

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1742-5468/2011/04/P04011

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.

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