Entanglement branching operator

TL;DR

This paper introduces an entanglement branching operator for tensor networks, enabling manipulation of entanglement structures and improving tensor network methods for many-body quantum systems.

Contribution

The paper presents a novel entanglement branching operator and demonstrates its applications in optimizing tensor networks and deriving new quantum states.

Findings

Enhanced tensor network optimization using entanglement branching.

Ability to disentangle tensors for improved tensor network states.

Derivation of projected entangled pair states from quantum states.

Abstract

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.