Tensor Network Renormalization

TL;DR

This paper presents a tensor network renormalization method that efficiently studies classical and quantum systems by removing short-range entanglement, enabling accurate analysis of critical phenomena and fixed points.

Contribution

It introduces a novel coarse-graining scheme using optimized tensors to remove short-range entanglement, improving the study of critical systems and fixed points in tensor networks.

Findings

Successfully applied to the 2D classical Ising model

Reveals scale invariance at criticality

Produces a sustainable renormalization group flow

Abstract

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement/correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.