Spin chains and vertex models based on superalgebras

基于超代数的自旋链和顶点模型

• 批准号: 281473820
• 负责人: Professor Dr. Holger Frahm
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 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/281473820?language=en
• 关键词: Spin; chains; vertex; models; based

Spin chains and two-dimensional vertex models with an underlying superalgebra structure appear naturally in certain statistical physics models, e.g. intersecting loops, and disordered electron systems. In several examples for such models the low energy effective theory describing their critical behaviour has displayed rather unusual properties: the lack of unitarity in these systems allows for continua of critical exponents leading to a fine structure with strong subleading corrections to scaling in the finite size spectrum. This is a signature of non-compact degrees of freedom emerging in the continuum limit of these models.In this project we plan to study the properties of these systems in the context of integrable superspin chains. In particular we want to identify the corresponding conformal field theories and characterize the continuous part of their spectrum. In addition, the effect of boundary conditions on the critical properties will be addressed. To deal with the strong finite-size effects present in these systems we shall develop new analytical methods for the analysis of the spectral problem.

自旋链和具有潜在超代数结构的二维顶点模型自然地出现在某些统计物理模型中，例如交叉环和无序电子系统。 在几个例子中，这种模型的低能量有效的理论描述其临界行为显示出相当不寻常的属性：在这些系统中缺乏统一性允许连续的临界指数导致一个精细的结构与强大的subleading修正缩放在有限尺寸的频谱。 这是在这些模型的连续极限中出现的非紧自由度的签名。在这个项目中，我们计划在可积超自旋链的背景下研究这些系统的性质。 特别是，我们要确定相应的共形场理论和表征其频谱的连续部分。 此外，还将讨论边界条件对临界性质的影响。 为了处理这些系统中存在的强有限尺寸效应，我们将开发新的分析方法来分析光谱问题。