Variational boundary based tensor network renormalization group

TL;DR

This paper introduces a variational boundary-based tensor network renormalization group method that improves accuracy in coarse-graining 2D tensor networks by optimizing boundary tensors, enabling higher-dimensional extensions with manageable computational costs.

Contribution

It presents a novel variational boundary tensor approach that enhances the accuracy of tensor network renormalization without increasing computational complexity.

Findings

Achieves higher accuracy than existing TRG methods.

Maintains the same computational complexity as original TRG.

Provides a practical pathway for extending TRG to higher dimensions.

Abstract

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.