Regular Article

Variational Monte-Carlo study of the extended Bose-Hubbard model with short- and infinite-range interactions

¹ Theoretical Physics, Saarland University, Campus E2.6, 66123 Saarbrücken, Germany
² École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

^a e-mail: bbogner@lusi.uni-sb.de

Received: 11 January 2019
Received in final form: 21 March 2019
Published online: 22 May 2019

Abstract

In this paper, we study the two-dimensional Bose-Hubbard model with short- and long-range interactions in the canonical ensemble. Using a Variational Monte-Carlo method, we obtain the phase diagrams containing four different phases: Mott insulator, density wave, superfluid and supersolid. The transition lines are determined using the structure factor and the superfluid density. We observe that the phase diagrams for short and long-range interactions are very similar quantitatively and qualitatively, but show also some significant differences. To evaluate the quality of our Variational approach, we compare our results with results published by other groups, obtained with various methods, such as an exact quantum Monte-Carlo algorithm and Gutzwiller Ansatz.