A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

Lode Pollet

doi:10.1016/j.crhy.2013.08.005

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder
[Une revue des simulations Monte Carlo pour le modèle de Bose–Hubbard avec désordre diagonal]

Lode Pollet ¹

¹ Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, University of Munich, Theresienstraße 37, 80333 Munich, Germany

Comptes Rendus. Physique, Disordered systems / Systèmes désordonnés, Volume 14 (2013) no. 8, pp. 712-724.

Abstract (VO)
Résumé

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.

Nous passons en revue la physique du modèle de Bose–Hubbard en présence de désordre dans le potentiel chimique, en portant notre attention sur des arguments analytiques récemment publiés en les combinant avec des simulations Monte Carlo quantiques. Mis à part les cas du superfluide et des phases isolantes de Mott qui peuvent advenir dans ce système sans désordre, le désordre conduit à une phase additionnelle, appelée verre de Bose. La topologie du diagramme de phases est contrainte par un théorème prouvant que la phase du verre de Bose doit intervenir entre le superfluide et lʼisolant de Mott, impliquant une transition de Griffiths entre ce dernier et le verre de Bose. Les diagrammes de phase complets en 3d et 2d sont discutés, et nous insistons sur lʼinsensibilité de la ligne de transition entre le superfluide et le verre de Bose au voisinage proche de lʼextrémité du lobe de lʼisolant de Mott. Nous commentons brièvement les connaissances établies et les questions qui demeurent dans le cas 1d, et présentons un rapide survol des travaux numériques sur les modèles liés.

Publié le : 2013-09-10

DOI : 10.1016/j.crhy.2013.08.005

Keywords: Bose–Hubbard, Superfluidity, Mott insulator, Bose glass, Monte Carlo simulations, Lifshitz tails
Mots-clés : Bose–Hubbard, Superfluidité, Isolant de Mott, Verre de Bose, Simulations Monte Carlo, Queues de Lifshitz

Affiliations des auteurs :

Lode Pollet ¹

¹ Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, University of Munich, Theresienstraße 37, 80333 Munich, Germany

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Lode Pollet. A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder. Comptes Rendus. Physique, Disordered systems / Systèmes désordonnés, Volume 14 (2013) no. 8, pp. 712-724. doi : 10.1016/j.crhy.2013.08.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.08.005/

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