Integrable anyon chains

在这个项目中，我们计划构建相互作用的非阿贝尔任意子的可积链，并研究其光谱和热力学性质，特别是它们的临界行为。 与使用这些链的量子自旋公式的更传统的方法不同，我们将专注于任意子公式。 这允许处理非整数量子维数的量子系统，它们在希尔伯特空间上没有自然的张量积结构。首先，我们将处理两种特定的任意子，它们具有与二面体群D3相关的内部对称性。 在边界条件下，这些物体的可积任意子链等价于显示这种对称性的量子自旋链。 后者的属性是很好的研究，从而允许直接比较这些对象的属性在不同的formulation.In另一部分，这个项目中，我们计划联合收割机的技术开发到一个框架，可用于构建和解决一般的内部对称性的任意链。

In this project we plan to construct integrable chains of interacting non-Abelian anyons and study the spectrum and thermodynamic properties, in particular their critical behaviour. Unlike in the more conventional approach using a quantum spin formulation of these chains we shall focus on the anyonformulation. This allows to deal with quantum systems with non-integer quantum dimension which have no natural tensor product structure on their Hilbert space.First, we shall deal with two specific species of anyons with an internal symmetry related to the dihedral group D3. Up to boundary conditions the integrable anyon chains for these objects are equivalent to quantum spin chains showing this symmetry. The properties of the latter are well-studied, thereby allowing a direct comparison of the properties of these objects in the different formulations.In another part of this project we plan to combine the techniques developed here into a framework which can be used to construct and solve anyonic chains with generic internal symmetries.