Emergent entanglement structures and self-similarity in quantum spin chains

TL;DR

This paper introduces a network-based approach to analyze many-body quantum states, revealing emergent entanglement structures, self-similarity, and community formations in quantum spin chains, thus providing new insights into quantum correlations.

Contribution

It presents a novel entanglement network representation for quantum states and uncovers emergent phenomena like self-similarity and community structures in spin chains.

Findings

Revealed symmetry in single-spin concurrence distributions.

Identified spatially localized entanglement communities.

Discovered cyclic self-similarity linked to community structure.

Abstract

We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localised communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding, and description of new physical phenomena even in models studied for decades.