Network Robustness: Detecting Topological Quantum Phases

TL;DR

This paper introduces a complex network analysis framework to detect topological phase transitions in quantum systems by examining changes in network robustness, revealing a homogeneous-heterogeneous transition invisible in real space.

Contribution

It presents a novel theoretical approach linking network robustness to topological phase transitions, providing a new way to characterize such transitions without symmetry breaking.

Findings

Network space undergoes a homogeneous-heterogeneous transition at the topological phase transition.

Network robustness analysis reveals phase transition features invisible in real space.

The framework can potentially be applied to various types of phase transitions.

Abstract

Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase transitions if the distinct phases do not break any symmetry, such as topological phase transitions. Here we present a novel theoretical framework established by complex network analysis for demonstrating that across a transition point of the topological superconductors, the network space experiences a homogeneous-heterogeneous transition invisible in real space. This transition is nothing but related to the robustness of a network to random failures. We suggest that the idea of the network robustness can be applied to characterizing various phase transitions whether or not the symmetry is broken.