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

在本计画中，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。这样的模型是无法访问的良好建立（分级）量子逆散射方法。特别是代数Bethe变换不能用于解决光谱问题，由于缺乏一个简单的参考状态。我们建议的重点是相互作用的无自旋费米子系统，即所谓的小极化子模型。添加非对角边界场，这个模型允许调查的基本问题，某些运输性能的这个和相关的模型。利用泛函Bethe近似方法，我们将确定自旋为1/2的可积链的基态和低能激发态，并计算由边界项引起的电流。第一步将采取对建设和解决类似的可积模型的粒子与额外的自由度，例如自旋。

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.