Optimization of tensor network states by means of a minimal principle and applications to quantum systems

张量网络态具有表达或近似给定量子态波函数的高势。对于每个局部张量的有效优化，张量周围环境的构建是重要的。在本研究中，我们重点研究了边界条件，即光滑边界条件，其中相互作用参数在系统边界处逐渐减小到零，双曲变形，其中参数增加到边界。这些条件被强加于一维自由或关联量子系统。在这些形变下，尽管哈密顿量不均匀，但相应的基态是均匀的，局域张量以均匀的方式优化。这一事实通过密度矩阵重整化群得到了证实，密度矩阵重正化群是优化局域张量的代表性数值工具。还报道了其他几个关于张量网络状态的试验。

The tensor network states has a hight potential of expressing or approximating a given quantum state wave function. For an efficient optimization of each local tensor, the construction of the environment around the tensor is important. In this study, we focus on the boundary condition, i.e. the smooth boundary condition, where the interaction parameter gradually decreases to zero toward the system boundary, the hyperbolic deformation, where the parameter increases to the boundary. These conditions are imposed to one dimensional free or correlated quantum systems. Under these deformation, despite of the non-uniformity in the Hamiltonian, the corresponding ground state is uniform, and the local tensors are optimized in a homogeneous manner. The fact is confirmed by means of the density matrix renormalization group, which is a representative numerical tool to optimize local tensors. Several other trials on the tensor network state are also reported.