Quantum Phase Diagram of Bosons in Optical Lattices
Abstract
We work out two different analytical methods for calculating the boundary of the Mott-insulator-superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from Quantum Monte-Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.
Cite
@article{arxiv.0806.2812,
title = {Quantum Phase Diagram of Bosons in Optical Lattices},
author = {F. E. A. dos Santos and A. Pelster},
journal= {arXiv preprint arXiv:0806.2812},
year = {2009}
}