Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks

TL;DR

This paper introduces a method to quantify the complexity of quantum states near critical points using complex network measures based on quantum mutual information, revealing high accuracy in identifying phase transitions.

Contribution

It applies complex network analysis to quantum mutual information to detect quantum phase transitions, a novel approach in quantum many-body physics.

Findings

Network measures accurately identify critical points in quantum models

Method works for different classes of quantum phase transitions

High finite-size scaling accuracy achieved

Abstract

We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of EEG/fMRI measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearson's correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, $Z_2$, mean field superfluid/Mott insulator, and a BKT crossover.