Transport properties of integrable quantum systems

降维和量子效应相互作用的一些最引人注目的结果是在输运中观察到的。可积模型具有无限多的局部守恒定律，预计将具有特别不寻常的输运性质。对于可积自旋1/2海森堡链，能量电流本身是守恒的，导致热传导无穷大。另一方面，自旋电流算符不是守恒的，但已知它与守恒电荷有有限的重叠，导致在有限温度下自旋德鲁德重为非零。然而，到目前为止，基于这些电荷的自旋德鲁德重量的Mazur界仅在无限温度下获得。本项目的目的有两个：(a)我们将从代数上构造与自旋电流算子有非零重叠的准局部电荷，并计算所有温度下相应的Mazur界。这些研究结果也有望与可积模型中的淬火动力学高度相关。(b)我们将基于融合代数方法中能级曲率的泛函方程计算全德鲁德权值。这种方法避免了以前基于热力学Bethe ansatz （TBA）计算的概念和技术问题，并将显示TBA结果是否有效。我们的分析结果将根据使用时变DMRG算法获得的数值数据进行检查。

Some of the most dramatic consequences of the interplay of reduced dimensionality and quantum effects are observed in transport. Integrable models, which have an infinite number of local conservation laws, are expected to have particularly unusual transport properties. For the integrable spin-1/2 Heisenberg chain the energy current itself is conserved leading to an infinite heat conductance. The spin current operator, on the other hand, is not conserved, but is known to have a finite overlap with conserved charges leading to a nonzero spin Drude weight at finite temperatures. So far, however, a Mazur bound for the spin Drude weight based on these charges has only been obtained at infinite temperatures.The aim of this project is twofold: (a) We will algebraically construct quasi-local charges which have a nonzero overlap with the spin current operator and evaluate the corresponding Mazur bound for all temperatures. The results of these investigations are also expected to be highly relevant for quench dynamics in integrable models. (b) We will calculate the full Drude weight based on functional equations for the energy level curvatures within a fusion algebra approach. This approach avoids the conceptual and technical issues of previous calculations based on the thermodynamic Bethe ansatz (TBA) and will show whether or not the TBA results are valid. Our analytical results will be checked against numerical data obtained using time-dependent DMRG algorithms.