Emptiness formation probability and quantum Knizhnik-Zamolodchikov equation
Emptiness formation probability and quantum Knizhnik-Zamolodchikov equation
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空洞形成概率与量子Knizhnik-Zamolodchikov方程
DOI：
10.1016/s0550-3213(03)00153-6
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
F. Smirnov
中科院分区：
文献类型：
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作者：
H. Boos;V. Korepin;F. Smirnov
我们考虑了零温零磁场下的一维XXX自旋1/2海森堡反铁磁体。我们感兴趣的是反铁磁基态中铁磁弦P(N)的形成概率。我们称之为空洞形成概率(EFP)。我们提出了一种计算非均匀情况下EFP的新方法。它基于量子克尼日尼克-扎莫罗奇科夫方程(QKZ)。在非均匀情况下，我们计算了n-⩽-6的等效流密度。齐次极限证实了我们关于量子关联和数论关系的假设。我们还对任意n的EFP的结构作了一个猜想。
We consider the one-dimensional XXX spin-1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability (EFP). We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik–Zamolodchikov equation (qKZ). We calculate EFP for n⩽6 for inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbitrary n.