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

本项目的主要目标是发展精确和有效地计算局部算子相关函数的方法不可积格模型。在以前的工作中，我们已经证明了自旋为1/2的海森堡链和相关可积模型的相关函数具有特定的结构，类似于自由费米子的威克定理，我们称之为“隐藏的费米子结构”：较长范围的相关函数是一点函数和邻域函数的多项式，其系数由基础无限维对称代数的表示理论决定。在这里，我们计划利用我们的经验与推导的通用functionalequations，以研究的问题，如果类似的隐藏的代数结构存在的更高自旋实现的可积海森堡链或可积晶格模型连接的仿射量子群的更高的秩。

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.