Effective-action approach to dirty bosons in optical lattices

Abstract

A system of cold bosonic atoms loaded in an optical lattice potential can undergo a macroscopic phase transition due to quantum fluctuations. As the depth of the lattice potential is increased, the ground state of the many-body system is found to go from a superfluid to a Mott-insulator state. In the presence of disorder a new phase intervenes in these transition: the Bose-glass phase. Usual analysis of this phase transition is made within the framework of mean-field theory. Such approximation predicts non-physical results for the condensate density. Taking into consideration the lack of precise analytical results in the literature, we propose the use of an effective-action approach for investigating such phase transition in the presence of disorder at arbitrary temperatures. These method, based on standard field-theoretical considerations, is used with the aim to improve the results of former analytical methods and provide better qualitative understanding of the quantum phase transition. We considered static diagonal disorder by means of a local chemical potential in the Bose-Hubbard model and obtained the phase boundary for homogeneous and Gaussian disorder distributions. We compared the condensate density predictions of our field theoretical effective-action method with the results of standard mean-field approximation. The application of the effective-action method showed to be promising in analyzing the superfluid to insulating states phase transition in the presence of disorder as well as in improving former analytical results.