We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener–Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited states of some integrable models, where the delta function represents a peak at the momentum of the excitation. As a concrete example of applications of our results, using the derived asymptotic formulas we compute the spin-correlation functions in the lowest energy band of the frustrated quantum XY chain in zero field, and the ground state magnetization.

我们发现 Toeplitz 行列式的渐近行为，其符号是两个贡献的总和：一个是围绕单位圆的环中的解析和非零函数，另一个与 Dirac delta 函数成比例。这些公式是通过使用 Wiener-Hopf 过程找到的。在计算某些可积模型的低激发态中的自旋相关函数时发现了这种类型的决定因素，其中 delta 函数表示激发动量处的峰值。作为我们结果应用的一个具体例子，使用推导的渐近公式，我们计算了零场中受挫量子XY链的最低能带中的自旋相关函数，以及基态磁化强度。