Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
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反铁磁大质量体系中XXZ链相关长度的低温谱
DOI：
10.1088/1751-8113/48/33/334001
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Suzuki
中科院分区：
文献类型：
--
作者：
M. Dugave;F. Göhmann;K. K. Kozlowski;J. Suzuki
量子传递矩阵形式化[25,26]为解析计算可积晶格模型的热力学性质[16,24]和相关函数[5,6,8,9]提供了一个框架。特别是，它可以计算可积海森堡链的相关长度[15 - 18,27]和相关的费米子模型[23]。本工作主要关注的是在有限磁场h和低温T下，即在大比h T下，计算反铁磁质量体系中XXZ链的全谱相关长度。上述引用的先前的工作处理的是无质量体系或h T较小的情况，主要局限于计算几个最大的相关长度。我们的研究是通过形式因子方法分析两点相关函数的低温行为，特别是它们的大距离渐近性的第一步，因为事实上，形式因子展开需要对一组完整的中间状态求和。最近，在无质量（或临界）状态下，对该模型进行了基于形状因子的低温下两点函数大距离渐近性分析[5,6]。在这项工作中，以及之前在形式因子方法中对基态相关函数的分析[12-14]中，有限磁场被证明是一个重要的正则化参数。只要磁场是有限的，基态以上的低能量激发就可以被归类为两个费米点附近的粒子-空穴激发，量子转移矩阵的“激发”也有类似的简单描述。当先使T和h趋于零时，我们发现我们的相关振幅公式[6]与Lukyanov在磁场消失时得到的基态显式公式[21]在数值上是一致的。我们希望类似的程序可以在大规模的制度下执行，并且我们将能够在某些特殊函数方面获得更明确的结果。这是可以预料的，因为在质量区域中没有费米点，而且自然进入相关函数描述的函数是周期或准周期的，具有周期或准周期π。事实上，在某些情况下，用顶点算子方法[10,20,22]得到的零温度和磁场下反铁磁质量区XXZ链形状因子的多重积分公式可以用封闭形式来计算。
The quantum transfer matrix formalism [25, 26] provides a framework for calculating the thermodynamic properties [16, 24] and correlation functions [5, 6, 8, 9] of integrable lattice models analytically. It enables, in particular, the calculation of correlation lengths of integrable Heisenberg chains [15–18, 27] and related Fermion models [23]. The main concern of this work is the calculation of the full spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime at finite magnetic field h and low temperature T, ie for large ratios h T. The above cited previous works dealt with the massless regime or with the case that h T is small and were mainly restricted to the calculation of a few largest correlation lengths. Our study is the first step in the analysis of the lowtemperature behaviour of two-point correlation functions, especially of their large-distance asymptotics, by means of a form factor approach, as, in fact, a form factor expansion requires the summation over a complete set of intermediate states. A form-factor based analysis of the large-distance asymptotics of two-point functions at low temperatures was recently completed for the model in the massless (or critical) regime 4 [5, 6]. In that work, as well as in the previous analysis of ground-state correlation functions within a form-factor approach [12–14], a finite magnetic field turned out to be an important regularization parameter. As long as the magnetic field is finite, the low-energy excitations above the ground state can be classified as particle-hole excitations about two Fermi points, and a similarly simple picture holds for the ‘excitations’ of the quantum transfer matrix as well. When sending first T and then h to zero we found numerical agreement of our formulae for the correlation amplitudes [6] with the explicit formulae obtained by Lukyanov [21] for the ground state at vanishing magnetic field.It is our hope that a similar program can be carried out in the massive regime and that we will be able to obtain even more explicit results in terms of certain special functions. This can be expected, since there are no Fermi points in the massive regime and since the functions that enter naturally into the description of correlation functions are periodic or quasi-periodic with period or quasi-period π. In fact, in some cases the multiple-integral formulae for the form factors of the XXZ chain in the antiferromagnetic massive regime at zero temperature and magnetic field, that were obtained within the vertex-operator approach [10, 20, 22], could be evaluated in closed form.
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影响因子：
3.7
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影响因子：
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DOI：
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影响因子：
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