Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains

Frank Göhmann, Karol K Kozlowski, Mikhail Minin
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引用次数: 2

Abstract

Abstract Evaluating a lattice path integral in terms of spectral data and matrix elements pertaining to a suitably defined quantum transfer matrix, we derive form-factor series expansions for the dynamical two-point functions of arbitrary local operators in fundamental Yang–Baxter integrable lattice models at finite temperature. The summands in the series are parameterised by solutions of the Bethe Ansatz equations associated with the eigenvalue problem of the quantum transfer matrix. We elaborate on the example of the XXZ chain for which the solutions of the Bethe Ansatz equations are sufficiently well understood in certain limiting cases. We work out in detail the case of the spin-zero operators in the antiferromagnetic massive regime at zero temperature. In this case the thermal form-factor series turn into series of multiple integrals with fully explicit integrands. These integrands factorize into an operator-dependent part, determined by the so-called Fermionic basis, and a part which we call the universal weight as it is the same for all spin-zero operators. The universal weight can be inferred from our previous work. The operator-dependent part is rather simple for the most interesting short-range operators. It is determined by two functions ρ and ω for which we obtain explicit expressions in the considered case. As an application we rederive the known explicit form-factor series for the two-point function of the magnetization operator and obtain analogous expressions for the magnetic current and the energy operators.
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可积量子链中局部算子动态两点函数的热形因子展开
摘要利用谱数据和适当定义的量子转移矩阵的矩阵元素计算晶格路径积分,导出了有限温度下基本Yang-Baxter可积晶格模型中任意局部算子的动态两点函数的形式因子级数展开式。该级数中的和由与量子转移矩阵的特征值问题相关的Bethe Ansatz方程的解参数化。我们详细讨论了XXZ链的例子,其中Bethe Ansatz方程的解在某些极限情况下可以很好地理解。我们详细地计算了零温度下反铁磁质量区自旋为零算子的情况。在这种情况下,热形状因子级数变成了具有完全显式积分的多重积分的级数。这些积分分解成一个与算子相关的部分,由所谓的费米子基决定,这个部分我们称之为泛权,因为它对所有自旋为零的算子都是一样的。通用权重可以从我们以前的工作中推断出来。对于最有趣的短程算子,算子相关部分相当简单。它由两个函数ρ和ω决定,在考虑的情况下,我们得到了它们的显式表达式。作为应用,我们重新导出了已知的磁化算符两点函数的显式形式因子级数,并得到了磁电流和能量算符的类似表达式。
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