Tensor Network Skeletonization

TL;DR

Tensor network skeletonization is a novel coarse-graining algorithm that efficiently simplifies tensor networks by removing short-range correlations, applicable to classical and quantum models across various dimensions.

Contribution

The paper introduces tensor network skeletonization, a new structure-preserving coarse-graining method for tensor networks, extending its application to higher dimensions and disordered systems.

Findings

Effective removal of short-range correlations at each scale.

New efficient representations of ground states for 1D and 2D quantum Ising models.

Applicable to disordered systems and higher-dimensional tensor networks.

Abstract

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations effectively at every scale. This approach is first presented in the setting of 2D statistical Ising model and is then extended to higher dimensional tensor networks and disordered systems. When applied to the Euclidean path integral formulation, this approach also gives rise to new efficient representations of the ground states for 1D and 2D quantum Ising models.