Correlation functions and the space of local operators in off-critical models and conformal quantum field theories

我们的项目有两个互补的主要目标，乍一看，它们可能看起来相当不相关。一方面，我们希望对XXZ量子自旋链的动力学相关函数有更深入的了解。对于这个模型，我们希望理解任意局部算子的动态两点函数的一般结构，我们希望通过有效和显式的形式因子序列表示来研究。后者将使我们能够在数值上和渐近上评估与应用相关的相关函数。另一方面，我们的目标是更好地理解量子场论中局部算子的空间，这可以解释为XXZ模型的缩放极限，或者更确切地说，是底层六顶点模型的缩放极限。从技术上讲，我们的两个看似不同的目标是通过费米子基方法联系起来的，费米子基方法在理解可积晶格模型和量子场论的相关函数方面取得了很大进展。

Our project has two complementary main objectives, which, at first sight, might look rather unrelated. On the one hand we wish to gain a deeper understanding of the dynamical correlation functions of the XXZ quantum spin chain. For this model we would like to understand the general structure of the dynamical two-point functions of arbitrary local operators which we would like to study by means of efficient and explicit form factor series representations. The latter will allow us to evaluate the correlation functions that are relevant in applications numerically as well as asymptotically. On the other hand, we aim at getting a better understanding of the space of local operators in quantum field theories that can be interpreted as scaling limits of the XXZ model, or rather of the underlying six-vertex model. Technically, our two seemingly different goals are connected by means of the Fermionic basis approach that has been behind much of the progress in the understanding of the correlation functions of integrable lattice models and quantum field theories in the recent past.