Spin chains and vertex models based on superalgebras

具有超代数结构的自旋链和二维顶点模型自然地出现在某些统计物理模型中，例如相交环路和无序电子系统。在这类模型的几个例子中，描述其临界行为的低能有效理论显示出相当不寻常的性质：这些系统中缺乏统一性，允许临界指数的连续，从而导致精细结构具有对有限尺寸谱中的标度的强子加载修正。这是在这些模型的连续体极限中出现的非紧致自由度的特征。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。特别地，我们想要确定相应的共形场论，并刻画其谱的连续部分。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，我们将发展新的分析方法来分析谱问题。

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.