标题： 赫维赛德反铁磁自旋-$\frac{1}{2}$链双线性自旋算符的精确渐近关联函数 显示英文标题

标题： Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain

摘要： 双线性自旋算符在海森堡反铁磁自旋-$\frac{1}{2}$链中的两点关联函数的均匀部分的精确渐近表达式被获得。 除了代数衰减外，还识别出对数贡献，并确定了数值系数。 我们还通过数值确认了双线性自旋算符的交错部分的乘法对数修正$\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3\delta_{a,b}-1) \ln^2r /(12 \pi^4 r^4)$，并将数值系数估计为$d\simeq 0.067$。 在本文的最后，讨论了我们的结果对于一维系统中贝雷津斯基-科尔斯特里茨-汤斯量子相变点处基态保真度敏感性的相关性。 显示英文摘要

摘要： Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3\delta_{a,b}-1) \ln^2r /(12 \pi^4 r^4)$, and estimate the numerical prefactor as $d\simeq 0.067$. The relevance of our results for ground state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.