Variational Cluster Perturbation Theory for Bose-Hubbard models

Details Variational Cluster Perturbation Theory for Bose-Hubbard models Variational Cluster Perturbation Theory for Bose-Hubbard models

2005-11-11

arxiv.org/abs/cond-mat/0511294v2

J. Phys.: Condens. Matter 18 (2006) 9525-9540

Physics

Condensed Matter

Other Condensed Matter

v1) 10 pages, 6 figures. v2) Final version as published

Scientific paper

10.1088/0953-8984/18/41/019

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.

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