Cluster update for tensor network states

TL;DR

This paper introduces a recursive tensor update method for tensor network states that improves accuracy over previous simple update schemes by employing finite-size cluster scaling, with successful benchmarking on a quantum spin model.

Contribution

It generalizes existing tensor update methods by incorporating cluster-based imaginary time evolution, enhancing accuracy in tensor network simulations.

Findings

Improved accuracy in tensor network state updates.

Successful benchmarking on a spin-1/2 antiferromagnetic model.

Accurate determination of magnetization and critical exponents.

Abstract

We propose a novel recursive way of updating the tensors in projected entangled pair states by evolving the tensor in imaginary time evolution on clusters of different sizes. This generalizes the so- called simple update method of Jiang et al. [Phys. Rev. Lett. 101, 090603 (2008)] and the updating schemes in the single layer picture of Pi\v{z}orn et al. [Phys. Rev. A 83, 052321 (2011)]. A finite-size scaling of the observables as a function of the cluster size provides a remarkable improvement in the accuracy as compared to the simple update scheme. We benchmark our results on the hand of the spin 1/2 staggered dimerized antiferromagnetic model on the square lattice, and accurate results for the magnetization and the critical exponents are determined.