Structural Search of the Multi-scale Entanglement Renormalization Ansatz with Parallel Tempering Approach

The Tensor Network (TN) method provides an effective and efficient framework for modeling quantum many-body states. Many previously proposed TN states have been constructed based on insights derived from certain entanglement laws. However, these states are ineffective from a variational space perspective when searching target states with spatially non-uniform entanglement structures, such as random spin and molecular systems. Therefore, to capture such entanglement structures, TN structural optimization is both required and crucial. In this research, we propose an optimal structure search method of Multi-scale Entanglement Renormalization Ansatz (MERA) being capable of flexible entanglement operations owing to its internal loop structure. However, It is tough to recombine tensors because of loops, so existing procedures for structural optimization of TN are limited to them without loops. We adopt sequentially brute-force searches within a selected range of two adjacent tensors consisting of MERA. Furthermore, we introduce the parallel tempering method to overcome the local minima and the disadvantage of not being able to evaluate the information of the entire structures for each local structural decision. Our approach showed that it could access the ground states of a multimer model where the original MERA can not access with the same bond dimensions.