Universal functional equations for spectrum, thermodynamics and correlation functions of integrable lattice models

本课题的主要目标是发展局部算子不可积格模型相关函数的精确有效计算方法。在之前的工作中，我们已经证明了自旋1/2海森堡链和相关可积模型的相关函数具有一个特定的结构特征，类似于自由费米子的ick定理，我们称之为“隐藏费米子结构”：较远距离的相关函数是单点函数和邻域相关器中的多项式，其系数由潜在的无限维对称代数的表示理论决定。在这里，我们计划利用我们在推导泛函方程方面的经验来研究是否存在类似的隐藏代数结构，用于可积海森堡链的高自旋实现或与高阶仿射量子群相连的可积晶格模型。

The main objective of this project is to develop methods for the exactand efficient calculation of correlation functions of local operators inintegrable lattice models. In previous work we have shown that thecorrelation functions of the spin-1/2 Heisenberg chain and of relatedintegrable models are characterized by a specific structure, similar toWick's theorem for free Fermions, which we have called a `hiddenFermionic structure': longer-range correlation functions arepolynomials in one-point functions and neighbour-correlators, whosecoefficients are determined by the representation theory of theunderlying infinite-dimensional symmetry algebra. Here we plan toutilize our experience with the derivation of universal functionalequations in order to study the question if similar hidden algebraicstructures exist for the higher-spin realizations of the integrableHeisenberg chains or for integrable lattice models connected withaffine quantum groups of higher rank.