Quantum phase transition of the transverse-field quantum Ising model on scale-free networks

TL;DR

This paper studies the quantum phase transition in the transverse-field quantum Ising model on scale-free networks, revealing mean-field behavior for certain degree exponents and non-mean-field universality classes for others.

Contribution

It provides the first analysis of quantum phase transitions on scale-free networks, identifying how universality classes depend on the network's degree exponent.

Findings

Mean-field behavior at $\lambda=6$

Non-mean-field universality for $\lambda=4.5$ and 4

Deviations increase as $\lambda$ decreases

Abstract

I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent $\lambda=6$, I obtain results that are consistent with the mean-field theory. For $\lambda=4.5$ and $4$, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. The deviation from the mean-field theory becomes more pronounced for smaller $\lambda$.