论文标题
Delta功能奇异性的Toeplitz决定因素的渐近行为
Asymptotic behavior of Toeplitz determinants with a delta function singularity
论文作者
论文摘要
我们发现Toeplitz决定因素的渐近行为具有两个贡献的总和：单位圆周围的一个环中一个分析和非零函数，而另一个与Dirac Delta函数成正比的。通过使用Wiener-HOPF程序可以找到该公式。这种类型的决定因素是在计算某些集成模型的低洼激发态中的自旋相关函数时发现的，其中三角洲函数代表激发动量处的峰值。作为我们结果应用的具体示例，使用衍生的渐近公式，我们计算了零场中沮丧的量子XY链的最低能带中的自旋相关函数和基态磁化。
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.
