Unveiling hidden features of the Kitaev model through a complex-network analysis

TL;DR

This paper applies a density matrix-based network analysis to the Kitaev chain, revealing hidden structural and entanglement features, including a topological phase transition point and a fully connected entanglement network.

Contribution

It introduces a novel network analysis method to uncover previously hidden features of the Kitaev model, connecting entanglement structure to topological phases and ground state factorization.

Findings

Identifies the critical point of the topological phase transition.

Discovers a singular point with uniform, nonzero entanglement across all fermion pairs.

Analyzes symmetry changes related to Majorana zero modes.

Abstract

We introduce a density matrix-based network analysis to explore the ground state of the Kitaev chain, uncovering previously hidden structural and entanglement features. This approach successfully identifies the critical point associated with the topological phase transition and reveals a singular point where the ground state exhibits uniform, nonzero entanglement between all fermion pairs, corresponding to a fully connected network structure. We provide an analytical explanation for this singular behavior and establish a connection to the concept of ground state factorization observed in spin chains. Moreover, we analyze the open chain scenario and observe characteristic symmetry changes in the ground state corresponding to Majorana zero modes. While complex network theory has been employed in the study of quantum systems before, we demonstrate that it can uncover fundamentally new physical insights.