Phase diagram of the Bose-Hubbard Model on Complex Networks

TL;DR

This paper investigates how the quantum phase transition of the Bose-Hubbard model is affected by complex network topologies, revealing the disappearance of the Mott-insulator phase under certain conditions in large networks.

Contribution

It demonstrates that the Mott-insulator phase of the Bose-Hubbard model vanishes in large complex networks with diverging degree moments or eigenvalues, extending understanding of quantum critical phenomena on networks.

Findings

Mott-insulator phase disappears when the second moment of degree distribution diverges.

Mott-insulator phase vanishes as the maximal eigenvalue of the adjacency matrix diverges.

Results extend to Apollonian scale-free networks embedded in 2D.

Abstract

Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed networks and we show that when the second moment of the average degree diverges the Mott-insulator phase disappears in the thermodynamic limit. Moreover we study the model on quenched networks and we show that the Mott-insulator phase disappears in the thermodynamic limit as long as the maximal eigenvalue of the adjacency matrix diverges. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.