Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
复制标题
XXZ 自旋 1/2 链无质量状态下动态相关函数的长距离大时间渐近行为
DOI：
10.1063/1.5094332
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发表时间：
2019
影响因子：
1.3
通讯作者：
K. Kozlowski
中科院分区：
文献类型：
--
作者：
K. Kozlowski
从最近得到的两点动力学关联函数的无质量形状因子展开出发，得到了这些关联子的长距离和大时间渐近性。
分析产生的临界指数和相关的振幅特征的渐近。
这些结果是在精确的和基于第一原理的考虑的基础上获得的：它们在任何阶段都不依赖于与场论或任何其他唯象方法的使用的某种假设对应。基于形状因子展开，该方法允许人们清楚地识别哪类激发态对渐近问题的贡献。所有这一切允许解决长期存在的问题的贡献的束缚态的两点函数的渐近性。例如，当考虑等时量子子的长距离m行为时，分析表明，虽然，\texit {in fine}，束缚态只产生在m中呈指数小的贡献，但它们在抵消某些幂律贡献方面也起着关键作用，这些幂律贡献如果存在，将明确打破长距离行为的普适性结构。
Starting from the massless form factor expansion for the two-point dynamical correlation functions obtained recently, I extract the long-distance and large-time asymptotics of these correlators.
The analysis yields the critical exponents and associated amplitudes characterising the asymptotics.
The results are obtained on the basis of exact and first principle based considerations: they \textit{do not rely, at any stage}, on some hypothetical correspondence with a field theory or the use of any other phenomenological approach. Being based on form factor expansion, the method allows one to clearly identify which contributions to the asymptotics issues from which class of excited states. All this permits to settle the long-standing question of the contribution of bound states to the asymptotics of two-point functions. For instance, when considering the long-distance $m$ behaviour of equal-time correlators, the analysis shows that while, \textit{in fine}, the bound states only produce contributions that are exponentially small in $m$, they also play a key role in cancelling out certain power-law contributions which, should they be present, would break explicitly the universality structure of the long-distance behaviour.
DOI：
10.1088/0305-4470/29/12/005
发表时间：
1996-01
期刊：
Journal of Physics A
影响因子：
--
作者：
M. Jimbo;T. Miwa
通讯作者：
M. Jimbo;T. Miwa
DOI：
10.1017/cbo9780511524332.002
发表时间：
1999-03
期刊：
--
影响因子：
--
作者：
Minoru Takahashi
通讯作者：
Minoru Takahashi