自由费米子模型中的晶格形状因子
Finite-lattice form factors in free-fermion models
摘要：
我们考虑有限周期格点上的一般$\mathbb{Z}_2$对称自由费米子模型，其中包括正方形和三角形格点上的伊辛模型和具有$n=2$的$\mathbb{Z}_n$对称BBS $τ^{(2)}$模型.翻译考夫曼的费米子的方法对角化的伊辛样转移矩阵的语言格拉斯曼积分，我们确定的转移矩阵的本征向量，并观察到，它们符合本征向量的正方形晶格伊辛转移矩阵。这允许找到统计模型和相关的有限长度量子链的自旋算子的精确有限晶格形状因子，其中最一般的是等价于横向场中的XY链。
英文摘要：
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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