Quantum Phase Diagram of Bosons in Optical Lattices

Details Quantum Phase Diagram of Bosons in Optical Lattices Quantum Phase Diagram of Bosons in Optical Lattices

2008-06-17

arxiv.org/abs/0806.2812v4

Physical Review A 79, 013614 (2009)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevA.79.013614

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.

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