Impurities and disorder in nearly integrable models

由于在固态系统和超冷气体中的实验实现，杂质在自旋1/2海森堡链中的影响最近重新引起了人们的兴趣。由于空间约束，杂质对一维磁激发谱和输运性质有很大影响。最小的一般散射体已经可以阻挡磁导，从而导致具有离散能量和特征边界相关性的有效隔离有限链段。令人惊讶的是，对于杂质对动量和频率分辨的动力结构因子的影响所知相对较少。一个基于有限链段的简单模型预测了弱无序极限的赝隙。这必须与随机键自旋链模拟的强无序极限形成对比，其中预测了发散的低能动态结构因子。现在，重要的是要考虑实验相关的热波动、最近邻的自旋耦合和杂质的磁性。在这个项目中，我们的目标是充分了解杂质对一维自旋链动力学结构因子的影响。连接有限链段的键，其他类型的杂质和有限温度将被考虑在内。最终我们将增加无序浓度，并研究弱无序到强无序随机单重态的交叉。

The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. Due to spatial confinement impurities have strong impact on the magnetic excitation spectrum and transport properties in one dimension. Already the smallest generic scatterer can block the magnetic conductance which leads to effectively isolated finite chain segments with discrete energies and characteristic boundary correlations. Surprisingly, relatively little is known about impurity effects on the momentum- and frequency resolved dynamical structure factor. A simple model based on finite chain segments predicts a pseudogap in the weak disorder limit. This must be contrasted to the strong disorder limit modelled by the random bond spin chain where a divergent low energy dynamical structure factor is predicted. Now it would be important to account for experimentally relevant thermal fluctuations, next-nearest neighbour spin couplings and magnetic properties of the impurities. In this project we aim for a full understanding of the effects of impurities on the dynamical structure factor of one-dimensional spin chains. Bonds linking the finite chain segments, other type of impurities and finite temperature will be taken into account. Eventually we will increase the disorder concentration and investigate the crossover from weak disorder to the strong disorder random singlet phase.