Phase diagram of the Bose-Hubbard model on complex networks

¹ Department of Physics, Northeastern University - Boston, MA 02115, USA
² Centre de Recerca en AgriGenomica, Universitat Autonoma de Barcelona - 08193 Bellaterra, Spain, EU
³ Dipartimento di Fisica, Università degli Studi di Parma - V.le G. P. Usberti 7/A, 43100 Parma, Italy, EU
⁴ Centro S3, CNR Istituto di Nanoscienze - Via Campi 213/a, 41100 Modena, Italy, EU

^a g.bianconi@neu.edu

Received: 7 March 2012
Accepted: 1 June 2012

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.