A comprehensive exploration of interaction networks reveals a connection between entanglement and network structure

TL;DR

This paper investigates how the structure of interaction networks influences eigenstate entanglement in quantum many-body systems, revealing correlations between network topology and entanglement properties, especially in irregular networks.

Contribution

It systematically explores all possible interaction networks up to seven spins, linking network structure to eigenstate entanglement and Hilbert space diagram features in the quantum Ising model.

Findings

Eigenstate entanglement depends on the Hilbert space diagram structure.

A correlation exists between the Hilbert space diagram and unconstrained spin pairs.

Minimum eigenstate entanglement is governed by the interaction network structure.

Abstract

Quantum many-body systems are typically studied assuming translational symmetry in the interaction network. Recent experimental advances in various platforms for quantum simulators have enabled the realization of irregular interaction networks, which are intractable to implement with conventional crystal lattices. Another hallmark of these advances is the ability to observe the time-dependent behaviour of quantum many-body systems. However, the relationship between irregular interaction networks and quantum many-body dynamics remains poorly understood. Here, we investigate the connection between the structure of the interaction network and the eigenstate entanglement of the quantum Ising model by exploring all possible interaction networks up to seven spins. We find that the eigenstate entanglement depends on the structure of the Hilbert space diagram, particularly the structure of the equienergy subgraph. We further reveal a correlation linking the structure of the Hilbert space diagram to the number of unconstrained spin pairs. Our results demonstrate that the minimum eigenstate entanglement of the quantum Ising model is governed by the specific structure of the interaction network. We anticipate that our findings provide a starting point for exploring quantum many-body systems with arbitrary interactions and finite system size. Moreover, our approach may be applicable to other quantum many-body systems, such as the Hubbard model.