Implementation of explicit SU(2)-invariance in tensor product states and applications to renormalization group calculations

该项目致力于量子信息理论的现代重整化群处理及其在相关电子系统中的应用以及它们的进一步发展。张量积态将用于研究一维和二维空间中的量子自旋系统，从而实现非阿贝尔su（2）-不变性。由于张量积态的局部因子由相当少的相关系数参数化，因此这种实现将极大地促进能量最小值的搜索。以这种方式，对于一个空间维度，可以直接访问物理极限。在两个空间维度的递归处理结合截断的本地辅助状态将被采用。该项目的主要目标是计算自旋为1/2的海森堡链的自相关函数和二维量子自旋系统的基态性质。作为一个副产品，我们期望一个有效的计算能量动量激发和一维系统的热力学。

The project is devoted to modern renormalization group treatments of quantum information theory and their application to correlated electronic systems as well as their further development. Tensor product states will be used for the investigation of quantum spin systems in one and two spatial dimensions with a consequent local implementation of the non-Abelian su(2)-invariance. This implementation will drastically facilitate the search of the energy minimum as the local factors of the tensor product states are parameterized by rather few correlation coefficients. In this way, for one spatial dimension the thermodynamical limit is directly accessible. In two spatial dimensions a recursive treatment combined with a truncation of the local auxiliary states will be employed. The main goalsof the project are the calculation of the auto-correlation function of the spin-1/2 Heisenbergchain and the ground-state properties of two-dimensional quantum spin systems. As a spin-off we expect an efficient calculation of the energy-momentum excitations and of the thermodynamics of one-dimensional systems.