Correlation functions of integrable lattice models and quantum field theories

可积晶格模型和量子场论的相关函数

• 批准号: 421428192
• 负责人: Professor Dr. Hermann Boos
• 金额: --
• 依托单位: Arbeitsgruppe Kondensierte Materie
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/421428192?language=en
• 关键词: Correlation; functions; integrable; lattice; models

The main objective of this project is the advancement of methods for the exact and efficient calculation of correlation functions of integrable lattice models and quantum field theories . In previous work we have shown that the correlation functions of the spin-1/2 Heisenberg chain and of related integrable models are characterized by a specific structure which we have called factorization: longer-range correlation functions are polynomials in one-point functions and neighbour-correlators, whose coefficients are determined by the underlying infinite-dimensional symmetry algebra. Here we want to show that the correlation functions of other integrable models factorize as well, and we want to extend the notion of factorization to the matrix elements occuring in the spectral representations of correlation functions. For the Heisenberg chain the factorization relied on the existence of a special 'Fermionic' basis of the space of local operators acting on the space of states of the spin chain. In the scaling limit it turns into a basis of the corresponding quantum field theory. Another goal of this project is to study the relation of the Fermionic basis of the field theory with the Verma module basis of the conformal field theory that determines its ultraviolet behaviour.

该项目的主要目的是进步的方法，用于确切有效地计算可集成晶格模型和量子场理论的相关函数。 在先前的工作中，我们已经表明，Spin-1/2 Heisenberg链和相关集成模型的相关函数的特征是我们称为分解的特定结构：更长范围的相关函数是单点函数和邻居相关器中的多项式函数，其系数通过无限的无限二次二定量表来确定其系数。在这里，我们要证明其他可集成模型的相关函数也分解，我们希望将分解概念扩展到相关函数的频谱表示中发生的矩阵元素。对于海森堡链，分解依赖于在自旋链状态空间上作用的本地操作员空间的特殊“费米子”基础。在缩放限制中，它变成了相应的量子场理论的基础。该项目的另一个目标是研究田间理论的费米子基础与确定其紫外线行为的保形场理论的Verma模块基础的关系。