Transition asymptotics of Toeplitz determinants and emergence of Fisher-Hartwig representations
Transition asymptotics of Toeplitz determinants and emergence of Fisher-Hartwig representations
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Toeplitz 行列式的过渡渐进和 Fisher-Hartwig 表示的出现
DOI：
10.1088/1361-6544/ab127a
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发表时间：
2019
期刊：
影响因子：
1.7
通讯作者：
Kozlowska K
中科院分区：
文献类型：
--
作者：
Kozlowska K
我们计算的过渡渐近（双标度限制）的Toeplitz行列式所产生的符号f t拥有Fisher-Hartwig奇点。我们考虑的符号f t依赖于一个参数t，使得f t在t> 0时有一个Fisher-Hartwig奇点，在t= 0时有两个Fisher-Hartwig奇点。与其他研究的过渡渐近的Toeplitz决定因素，我们的设置涉及的出现费舍尔-Hartwig表示。我们使用正交多项式的Riemann-Hilbert问题及其与Painlevé超越的联系来获得渐近性。我们应用我们的结果来研究一个特殊的相关器称为空形成概率（EFP）的一维各向异性XY自旋-1/2链在横向磁场中，并描述其在相图中的不同区域之间的过渡跨越临界线。
We compute the transition asymptotics (double-scaling limits) of Toeplitz determinants generated by symbols f t possessing Fisher–Hartwig singularities. The symbols f t that we consider depend on a parameter t such that f t has one Fisher–Hartwig singularity when t> 0 and two Fisher–Hartwig singularities when t= 0. Unlike in the other studies of the transition asymptotics of Toeplitz determinants, our setting involves the emergence of Fisher–Hartwig representations as. We use the Riemann–Hilbert problem for orthogonal polynomials and its connection to Painlevé transcendents to obtain the asymptotics. We apply our results to study a special correlator known as the emptiness formation probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field, and describe its transition between different regions in the phase diagram across critical lines.