Simulating many-body quantum systems on a classical computer is a difficult problem whose computational complexity grows exponentially with the size of the system. Tensor Networks is a framework which breaks down large tensors into a network of smaller tensors and allows an efficient simulation of certain many-body quantum systems. However, to calculate expectation values of local observables a contraction of the entire network is needed. This is a known hard problem for 2D systems, and a major bottleneck in all tensor-network based algorithms.
In this work we approximate this contraction using a new method called "Block Belief-Propagation", an algorithm which coarse-grains the system into blocks of tensors and performs belief propagation between the blocks, to get an effective environment of each block. I will demonstrate how this algorithm can be applied to the anti-ferromagnetic Heisenberg model on the Kagome lattice in the thermodynamic limit - a frustrated 2D model that is difficult to simulate using existing numerical methods. | 
