Functional Bethe ansatz methods for superspin chains: treatment of boundary fields and transport problems

超自旋链的功能贝特方法：边界场和传输问题的处理

• 批准号: 66577966
• 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 Grants
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/66577966?language=en
• 关键词: Functional; Bethe; ansatz; methods; superspin

In this project we plan to study the effect of boundary conditions which break particle number conservation on the low-energy spectrum of integrable superspin chains. Such models are not accessible to the well established (graded) quantum inverse scattering method. In particular the algebraic Bethe ansatz cannot be used to solve the spectral problem due to the absence of a simple reference state. The focus of our proposal is on a system of interacting spinless fermions, the so-called small polaron model. Adding non-diagonal boundary fields to this model allows to investigate basic questions related to certain transport properties of this and related models. Using functional Bethe ansatz methods developed before for integrable spin-1/2 chains we shall determine the ground state and low energy excitations and compute the current induced by the boundary terms. First steps will be taken towards the construction and solution of similar integrable models for particles with additional degrees of freedom, e.g. spin.

在这个项目中，我们计划研究打破粒子数守恒的边界条件对可积超自旋链低能谱的影响。这样的模型不能被公认的(分级的)量子逆散射方法所访问。特别是，由于没有一个简单的参考态，代数Bethe ansatz不能用来解决谱问题。我们提议的重点是一个相互作用的无自旋费米子系统，即所谓的小极化子模型。在该模型中加入非对角边界场，可以研究与该模型及相关模型的某些输运性质有关的基本问题。用泛函Bethe ansatz方法计算可积自旋1/2链的基态和低能激发，并计算由边界项引起的电流。第一步是建立和求解具有额外自由度的粒子的类似可积模型，例如自旋。

项目成果

Truncation identities for the small polaron fusion hierarchy

• DOI: 10.1088/1367-2630/15/4/043026
• 发表时间: 2012-11
• 期刊: New Journal of Physics
• 影响因子: 3.3
• 作者: Andr'e M. Grabinski;H. Frahm