标题： XX链在开放边界条件下的纠缠熵中的普遍奇偶效应 显示英文标题

标题： Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

摘要： 我们考虑在存在磁场的情况下，具有开放边界条件的一维XX自旋链中的Renyi纠缠熵。 在半无限系统且块从边界开始的情况下，我们基于关于Toeplitz加Hankel矩阵行列式的最近数学定理，严格推导出大块尺寸的渐近行为。 我们猜想该行列式渐近行为修正的广义Fisher-Hartwig形式，该形式允许对任意n阶o(1/l)的标度修正进行精确表征。 通过将这些结果与共形场论论证相结合，我们还推导出具有开放边界条件的有限链以及块与边界分离的情况下的精确表达式。 显示英文摘要

摘要： We consider the Renyi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher-Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(1/l) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary.