Automatic structural optimization of tree tensor networks

The tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where structure defined by connectivity isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose TTN algorithm that enables us to automatically optimize local reconnections isometries suppress bipartite entanglement entropy on their legs. can be seamlessly implemented such conventional approach as density-matrix renormalization group. We apply inhomogeneous antiferromagnetic Heisenberg spin chain, having hierarchical spatial distribution interactions. then demonstrate embedded ground state system efficiently visualized perfect binary optimized TTN. Possible improvements and applications are also discussed.