Mott-insulator–to–superfluid transition in the Bose-Hubbard model: A strong-coupling approach

Abstract

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive HubbardStratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

“…Again, similar results, e.g., the correlator b † µbν ground can also be obtained employing other methods, such as the the random phase approximation [88]. However, the justification of this approximation is another matter -especially for time-dependent situations we are interested in, such as a rapidly changing J(t) and the subsequent dephasing of quasi-particles etc.…”

“…(24)- (26). This expression (31) has already been derived using different methods, such as the time dependent Gutzwiller approach [87], the random phase approximation [88], or the slave boson approach [89], where…”

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

“…A self-consistent RPA calculation of the density in the "vacuum" state, where we approximate the single boson tight-binding density of states (DOS) as a constant within the band of width 8t (g(ǫ) = 1/8t), can be carried out exactly [for the simplified case where only two bosonic states (occupancies 0 and 1) are retained at each site], and yields the following expression which is indeed of the scaling form in Eq. (15).…”

“…Approximate analytical calculations that do not significantly compromise on the quality of the results, are of great value as they are computationally less demanding, and can provide a better understanding of the dominating physical processes for experimental parameters of interest. While there have also been many analytical approaches to the Bose-Hubbard Model [10][11][12][13][14][15][16][17], to our knowledge, none of them do a good job of giving the density distribution throughout the trap for finite temperature and large interaction strength U .…”

Slave-particle approach to the finite-temperature properties of ultracold Bose gases in optical lattices

“…By varying the parameters such as the density and the external potential, the system would undergo a quantum phase transition and evolve from the superfluid phase to Mott-insulating phase. In the past, various theoretical approaches have been used to investigate this superfluid/Mott-insulator transition at zero temperature such as the strongcoupling expansion [6,7,8,9], Gutzwiller projection ansatz [4,10,11,12], quantum Monte Carlo simulations [13,14], and other mean-field approximations [5,15,16]. By comparison, there are less studies focusing on the nonzero temperature properties [16,17,18,19,20,21], and this will be the main topic of this paper.…”