#### Condensed Matter Theory

### Niklas Teichmann et.al.: Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

**Author(s)**:**Niklas Teichmann, Dennis Hinrichs, Martin Holthaus, André Eckardt****Title**:**Date of Upload**: 2009-06-15
**Article**:**Phys. Rev. B 79, 224515 (2009), American Physical Society (APS)****Keywords**: Bose-Hubbard model, high-order perturbation theory, process-chain approach, correlation function, phase diagram, Mott insulator, superfluidity, mean-field limit**PACS**: 67.85.Hj, 64.70.Tg, 03.75.Lm, 03.75.Hh**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.
**URL: http://de.arxiv.org/abs/0904.0905 (text/html)**

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

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