Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

TL;DR

This paper introduces coarse-graining tensor renormalization algorithms for finite periodic lattices, improving the accuracy of physical property calculations in 2D lattice models like Ising and Kitaev models.

Contribution

It presents two novel coarse-graining strategies and a sweeping scheme for global optimization within tensor network models, enhancing finite-size lattice computations.

Findings

Finite-size algorithms outperform infinite-size ones in accuracy.

The methods successfully applied to Ising and Kitaev models.

Algorithms achieve high precision in finite lattice simulations.

Abstract

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor-network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.