Quantum phase transitions of ultracold Bose systems in nonrectangular optical lattices

Abstract

In this paper, we investigate systematically the Mott-insulator-superfluid quantum phase transitions for ultracold scalar bosons in triangular, hexagonal, and Kagomé optical lattices. With the help of the field-theoretical effective potential, by treating the hopping term in the Bose-Hubbard model as perturbation, we calculate the phase boundaries analytically for different integer filling factors. Our analytical results are in good agreement with recent numerical results.

Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice

“…Critical values of U/J for the formation of both the n = 1 and n = 2 Mott insulators in a zero-temperature homogeneous system have been calculated using a high-order perturbation method. These calculated critical values in the 2D triangular and kagome lattices have the ratio 1.65, in disagreement with the scaling prediction [23]. Yet, we cannot compare these calculations directly to our experimental findings because they do not account for inhomogeneity or non-zero temperature.…”

Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

“…In the case of ∆µ = 0, the phase boundaries of superlattice systems . [51](effective-potential Landau theory) to determine the location of seconde-order phase transition boundaries for high-dimensional single-component bose systems, such as square and cubic lattice as well as triangular, hexagonal and kagomé lattice [49], but they make an easy mistake on the details for obtaining the phase boundaries equations. In F. E. A. dos Santos et al's work [51], if the equation…”

“…So, it's not the right way (solving the equation 1/c 2 (t) = 0 by the series expanding 1/c 2 (t)) to obtain the phase boundaries in F. E. A. dos Santos et al's work [51]. The correct phase boundaries [49,52,53] is given by…”

Visibility of ultracold Bose system in triangular optical lattices

“…In order to compare our analytical result with their experimental observation, the third dimension has to be taken into account. Due to the orthonormality of the Wannier function, the third dimension would not affect the in-plane hopping parameter, J can be calculated explicitly from the lattice potential (7) and the Wannier function (8) via Eq. ( 5), it reads…”

“…In our previous work [7], we have calculated the phase boundaries of MI-SF quantum phase transitions of ultra-cold bosons in triangular, hexagonal, as well as Kagomé optical lattices analytically via the method of the field-theoretical effective potential [8], the relative deviation of our analytical results from the numerical results [9] is less than 10%. However, these results cannot be compared with the experimental observation, since the phase boundaries of the ultra-cold system are not able to be detected directly in experiments.…”