Tensor Network States with Three-Site Correlators

TL;DR

This paper extends the Complete Graph Tensor Network States (CGTNS) approach by incorporating three-site correlators, analyzing their impact on accuracy and efficiency in modeling spin states of manganocene.

Contribution

Introduces and compares three strategies for integrating 3-site correlators into CGTNS, optimizing the balance between accuracy and variational space size.

Findings

CGTNS with 3-site correlators achieves high accuracy with reduced variational space

Selective inclusion of significant 3-site correlators improves efficiency

All investigated parameterizations have distinct advantages and limitations

Abstract

We present a detailed analysis of various tensor network parameterizations within the Complete Graph Tensor Network States (CGTNS) approach. We extend our 2-site CGTNS scheme by introducing 3-site correlators. For this we devise three different strategies. The first relies solely on 3-site correlators and the second on 3-site correlators added on top of the 2-site correlator ansatz. To avoid an inflation of the variational space introduced by higher-order correlators, we limit the number of higher-order correlators to the most significant ones in the third strategy. Approaches for the selection of these most significant correlators are discussed. The sextet and doublet spin states of the spin-crossover complex manganocene serve as a numerical test case. In general, the CGTNS scheme achieves a remarkable accuracy for a significantly reduced size of the variational space. The advantages, drawbacks, and limitations of all CGTNS parameterizations investigated are rigorously discussed.