Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus, and André Eckardt
Phys. Rev. B 79, 224515 – Published 12 June 2009

Abstract

We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made possible by a diagrammatic process-chain approach, derived from Kato’s representation of the many-body perturbation series, which can be implemented numerically in a straightforward manner. We compute ground-state energies, atom-atom correlation functions, density-density correlations, and occupation number fluctuations, for one-, two-, and three-dimensional lattices with arbitrary integer filling. A phenomenological scaling behavior is found which renders the data almost independent of the filling factor. In addition, the process-chain approach is employed for calculating the boundary between the Mott insulator phase and the superfluid phase with high accuracy. We also consider systems with dimensionalities d>3, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.

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  • Received 1 April 2009

DOI:https://doi.org/10.1103/PhysRevB.79.224515

©2009 American Physical Society

Authors & Affiliations

Niklas Teichmann*, Dennis Hinrichs, and Martin Holthaus

  • Institut für Physik, Carl von Ossietzky Universität, D-26111 Oldenburg, Germany

André Eckardt

  • ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain

  • *teichmann@theorie.physik.uni-oldenburg.de

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Vol. 79, Iss. 22 — 1 June 2009

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