Loop optimization for tensor network renormalization

TL;DR

This paper presents a tensor renormalization group scheme that deforms 2D tensor networks into loops for improved accuracy and stability in coarse-graining classical and quantum systems.

Contribution

The paper introduces a novel loop optimization method for tensor network renormalization, enhancing accuracy and stability in classical and quantum models.

Findings

Effective in classical Ising model

Applicable to frustrated 2D quantum systems

Improves accuracy and stability of renormalization flow

Abstract

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.