有质量可积量子场论中的有限温度动力学关联
Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
摘要：
考虑可积量子场论中局域算符的有限温度、频率和动量相关的两点函数。我们专注于零温度关联函数的情况下，主要由单粒子模式的相干传播所产生的δ函数线。我们的具体例子是量子伊辛模型和O（3）非线性西格玛模型无序相中自旋场的两点函数。我们采用一个莱曼表示在已知的精确零温度形状因子进行低温展开的两点函数。我们提出了两种不同但等效的方法来正则化莱曼展开中存在的发散：一种直接调节无限体积中矩阵元素平方的积分表达式，而另一种通过减去大的有限体积中的发散来操作。我们的中心结果是，线形状的温度加宽表现出明显的不对称性和最大向上的能量（“温度相关的间隙”）的移位。本文给出的场论结果描述了量子伊辛链和整数自旋海森堡链中动力学结构因子的标度极限。我们讨论了相关的非弹性中子散射实验的分析结果，如CsNiCl 3和YBaNiO 5的带隙自旋链系统。
英文摘要：
We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.
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