Algorithms for tensor network renormalization

TL;DR

This paper details algorithms for tensor network renormalization (TNR), enabling efficient contraction of tensor networks in classical and quantum many-body systems, with demonstrated accuracy at critical points.

Contribution

It provides a comprehensive description of TNR algorithms and benchmarks their effectiveness on classical and quantum models, especially at criticality.

Findings

TNR maintains high accuracy over multiple coarse-graining steps.

TNR effectively handles critical points in models.

Algorithms are applicable to both classical and quantum systems.

Abstract

We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D classical many-body system or the Euclidean path integral of a 1D quantum system can be represented as a network of tensors, before describing how TNR can be implemented to efficiently contract the network via a sequence of coarse-graining transformations. The efficacy of the TNR approach is then benchmarked for the 2D classical statistical and 1D quantum Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining transformations, even at a critical point, is demonstrated.