Emergent entanglement structures and self-similarity in quantum spin chains

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.

Identifying correlation clusters in many-body localized systems

“…Graph theory has been used in the past to detect quantum phase transition in equilibirum settings [54][55][56]. Recently, another work identified the so called "ergodic bubbles" (i.e.…”

Emergent complex quantum networks in continuous-variables non-Gaussian states

“…In particular, emergent complex networks based on quantum mutual information have determined critical points for quantum phase transitions [36,43]. Likewise, complex network theory has been successful in determining self-similarity in entanglement structure of spin-chains [44] as well as new kinds of structured entanglement emerging from quantum cellular automata [45] on qubit/gate/ciruit-based quantum computers. Networks are naturally evoked in the quantum regime in relation to the quantum internet [46] but they are pivotal in all quantum technologies.…”