Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

TL;DR

This paper introduces a new tensor network contraction method using corner transfer matrix renormalization group for various 2D lattices, demonstrating accurate results on classical Ising models and potential for quantum models.

Contribution

A novel tensor network contraction technique applicable to diverse 2D lattice geometries, validated on classical models and promising for quantum systems.

Findings

Accurate contraction results for classical Ising models on multiple lattices

Method shows excellent agreement with literature benchmarks

Potential applicability to quantum lattice models with wave-function optimization

Abstract

We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of triangular, kagome, honeycomb, square-octagon, star, ruby, square-hexagon-dodecahedron, and dice lattices. As benchmark tests, we apply the developed method to the classical Ising model on different lattices and observe a remarkable agreement of the results with the available from the literature. The approach also shows the necessary potential to be applied to various quantum lattice models in a combination with the wave-function variational optimization schemes.