Mean-field phase diagram of cold lattice bosons in disordered potentials

Abstract

We show that a site-dependent mean-field approach captures the quantum phases of the disordered Bose-Hubbard model commonly adopted to describe ultracold bosons in random optical lattice potentials. The different phases, namely superfluid, Mott insulator, Bose-glass and -- at finite temperature -- normal fluid, are characterized by means of the superfluid and condensate fractions, and compressibility of the system. We point out that both the boundaries of the Mott lobes and the nature of the phase surrounding them are related to the spectral features of a purely off-diagonal non-interacting Anderson model. We compare our results to other works.Comment: 5 pages, 4 figures, added some references and reformulated some sentence

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

“…[52], and further developed in [54], where the boundary of the Mott lobe was linked to the stability of the zero solution of the self-consistency equations, which is then studied through linearization of those equations. Moreover the authors suggest that the presence of the BG surrounding the MI phase could be inferred from the spectral properties of the random matrix, which appear in the linearized problem.…”

“…Our main results are: i) for the Hamiltonian H 1 there is a direct MI-SF transition at the tips of the Mott lobes in the thermodynamic limit; ii) for the Hamiltonian H 2 the Mott lobes are smaller, and the direct MI-SF transition at their tips disappears, although the region of BG is very narrow; iii) finally, for H 3 there is no direct MI-SF transition and the region of BG is wider in comparison to H 2 . One of the main aspects of this paper is also the use of the mean-field theory combined with the simple Hartree-Fock approach, quite different from what has been proposed so far [52][53][54][55][56][57][58], and quite efficient in determining the phase boundary between the BG and the SF phase.…”

Dark solitons near the Mott-insulator–superfluid phase transition

“…A generalized Bogoliubov-de Gennes stability analysis indicates that the solitons are sensitive to perturbations and thereby break down over longer time periods. Our results are achieved by employing the position-dependent Gutzwiller ansatz which gives a satisfactory description of the quantum phases of inhomogeneous bosonic systems [27,28] as well as their dynamical behavior [29]. We note that the same method was recently utilized to study vortices in the vicinity of the MI-SF phase transition [26,30].…”

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

“…[28]. GMFT provides qualitatively correct phase diagrams for strongly interacting clean [40][41][42][43] and disordered [44][45][46][47][48] (away from the tip of the Mott lobe) systems. It has also been used to study nonequilibrium effects such as the dynamical generation of molecular condensates [49] and MIs [50], dipole oscillations [51], quantum quenches [48,52,53], expansion dynamics [54,55], and transport in the presence of disorder [48,56].…”