Renormalization of tensor networks using graph independent local truncations

TL;DR

This paper presents a new, efficient tensor network renormalization algorithm that reduces bond dimensions without altering network geometry, applicable to various networks and suitable for higher-dimensional real-space RG.

Contribution

The authors introduce a graph-independent local truncation method for tensor networks, enabling efficient bond dimension reduction and RG flow implementation across different network geometries.

Findings

Achieves accuracy comparable to top existing methods on 2D Ising model

Low computational cost and simple to implement

Applicable to higher-dimensional networks, including 3D

Abstract

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a tensor network coarse-graining algorithm, it yields a proper renormalization group (RG) flow. Compared to existing methods, the advantages of our algorithm are its low computational cost, simplicity of implementation, and applicability to any network. We benchmark it by evaluating physical observables for the 2D classical Ising model and find accuracy comparable with the best existing tensor network methods. Because of its graph independence, our algorithm is an excellent candidate for implementation of real-space RG in higher dimensions. We discuss some of the details and the remaining challenges in 3D. Source code for our algorithm is freely available.