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，这两个目标可能看起来很不相关。一方面，我们希望对XXZ量子自旋链的动力学关联函数有更深入的了解。对于这个模型，我们想了解的一般结构的动力学两点函数的任意本地运营商，我们希望通过有效的和明确的形式因子系列表示研究。后者将使我们能够评估的相关函数是相关的应用程序的数值以及渐近。另一方面，我们的目标是更好地理解量子场论中的局部算子空间，这些空间可以被解释为XXZ模型的标度极限，或者更确切地说，是底层六顶点模型的标度极限。从技术上讲，我们的两个看似不同的目标是通过费米基方法连接起来的，费米基方法是近年来在理解可积晶格模型和量子场论的相关函数方面取得的许多进展的背后。

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.