Tensor renormalization group approach to 2D classical lattice models

TL;DR

This paper introduces a tensor renormalization group method for 2D classical lattice models, inspired by quantum entanglement concepts, and demonstrates its effectiveness on the triangular lattice Ising model.

Contribution

It presents a novel tensor renormalization group technique that combines classical and quantum ideas, offering a new approach to analyze 2D lattice models.

Findings

Accurately computed magnetization of the triangular lattice Ising model.

Demonstrated the method's potential as an alternative to traditional renormalization techniques.

Showed the approach's basis in quantum entanglement theory enhances classical model analysis.

Abstract

We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of DMRG. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.