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arXiv:1304.2634 · Physical Review A

Generalized effective-potential Landau theory for bosonic quadratic superlattices

Tao Wang, Xue‐Feng Zhang, Sebastian Eggert, Axel Pelster

Published Jun 17, 2013• 13 citations
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Abstract

We study the properties of the Bose-Hubbard model for square and cubic superlattices. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multiple components and not only find the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. A comparison of our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective-potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.

DOI
10.1103/physreva.87.063615

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We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.
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.
We derive the Bogoliubov+U\mathrm{Bogoliubov}+UBogoliubov+U formalism to study the thermodynamical properties of the Bose-Hubbard model. The framework can be viewed as the zero-frequency limit of bosonic dynamical mean-field theory (B-DMFT), but equally well as an extension of the mean-field decoupling approximation in which pair creation and annihilation of depleted particles is taken into account. The self-energy on the impurity site is treated variationally, minimizing the grand potential. The theory containing just three parameters that are determined self-consistently reproduces the T=0T=0T=0 phase diagrams of the three-dimensional and two-dimensional Bose-Hubbard model with an accuracy of 11%1 or better. The superfluid to normal transition at finite temperature is also reproduced well and only slightly less accurately than in B-DMFT.