Single-layer tensor network approach for three-dimensional quantum systems

TL;DR

This paper introduces a simplified method for calculating observables in three-dimensional quantum systems using tensor networks, leveraging their multi-layer structure to improve efficiency and accuracy.

Contribution

The authors develop a novel approach that exploits the multi-layer structure of tensor networks to simplify contractions in 3D quantum systems, enabling higher bond dimensions.

Findings

Achieved bond dimension D=7 on cubic lattice Heisenberg model

Obtained results that agree well with previous studies

Demonstrated the effectiveness of the layer-based contraction method

Abstract

Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to largely simplify the contraction. The proposed approach involves the usage of the layer structure both to simplify the search for the boundary projected entangled pair states and the single-layer mapping of the final corner transfer matrix renormalization group contraction. We benchmark our results on the cubic lattice Heisenberg model, reaching the bond dimension D = 7, and find a good agreement with the previous results.