Size consistency of tensor network methods for quantum many-body systems

TL;DR

This paper emphasizes the importance of size consistency in tensor network methods for quantum many-body systems, showing it is crucial for their effectiveness and independent of entanglement criteria.

Contribution

It establishes size consistency as a necessary condition for tensor network methods and clarifies its independence from entanglement criteria.

Findings

Size consistency is essential for tensor network success.

Size consistency is independent of entanglement criteria.

Provides a general constraint for tensor network construction.

Abstract

Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an efficient tensor network, and thus the variational space, is a subtle problem and the main obstacle of the method. We demonstrate the necessity of size consistency in tensor network methods for their success in addressing the quantum many-body problem. We further demonstrate that size consistency is independent of the entanglement criterion, thus providing a general and tight constraint to construct the tensor network method.