Renormalization group contraction of tensor networks in three dimensions

TL;DR

This paper introduces a new tensor network contraction method based on renormalization group principles, emphasizing exact coarse graining before truncation, and demonstrates its effectiveness in 2D and 3D systems.

Contribution

It proposes a novel RG-inspired contraction strategy for tensor networks in arbitrary geometries, with a focus on exact coarse graining before controlled truncation.

Findings

Benchmark in 2D shows high accuracy compared to exact contraction.

Method successfully applied to 3D tensor networks.

Emphasizes the importance of exact RG steps for entanglement management.

Abstract

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three dimensional system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.