Phase diagram of trapped bosons in a kagome lattice—application of inhomogeneous mean field theory

Abstract

Motivated by the possibility of obtaining a trimerized optical lattice, such as a kagome lattice experimentally by employing counter propagating laser beams, we investigate the phase diagram of correlated bosons in a kagome lattice in the presence of a harmonic confinement.To study the phase diagram, we compute the order parameters of an extended Bose-Hubbard model which is solved via the standard mean field technique in the presence of a trapping potential. It is emphasized that such trapping effects (together with the density exchange term) lead to the necessity of considering the detailed geometry of the lattice, and thus the measured quantities appeal to a particular geometry, kagome lattice being the case here. The phase diagram thus obtained yields co-existence of different compressible and incompressible phases. There are distinct signatures of superfluid, insulating, density ordered and supersolid phases as one moves towards the edge of the lattice starting from the centre of the confining potential. A comparison of the results obtained for the order parameters corresponding to other geometries, such as square and honeycomb lattices are presented. Relevant to the time-of-flight experiments, the order parameters have been computed in the momentum space, which corroborate the existence of different phases for a kagome lattice.

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

“…In the ferromagnetic case, the variations of ψ i and ρ i are in complete agreement with the results obtained in Refs. [52,55]. We have also checked the spin eigenvalues and the order parameter profiles in presence of one dimensional trapping potential without zV /U 0 in both the AF and ferromagnetic cases are in agreement with the results obtained in Ref.…”

“…[61,65]. We have also checked the spin eigenvalues and the order parameter profiles in presence of one dimensional trapping potential without zV/U 0 in both the AF and ferromagnetic cases are in agreement with the results obtained in ref.…”

“…In the ferromagnetic case, we have checked that the Fourier transform profiles are in agreement with those in refs. [61,65].…”

Mean-field study of the Bose-Hubbard model in Penrose lattice

“…Link configuration of distinct vertexes in Penrose lattice. Listed are index α determined in the present work, the total number of paths using k links, M k (k = 1, 2, 3), the number of vertexes having l links, to which one can access using k links, m 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 m (5) 1 3 3 3 1 1 1 2 2 2 2 2 2 2 2 0 0 0 1 1 1 1 0 0 0 5 3 1 m (6) 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 m (7) 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 M2 15 15 15 15 16 16 16 17 17 17 17 16 16 16 15 15 15 17 17 17 17 18 19 21 25 24 23 m (3) 2 11 10 9 9 12 12 11 15 14 14 13 6 5 4 0 0 0 0 0 0 0 3 5 10 20 10 2 m note that this self-consistent procedure gives moderately accurate results as compared with quantum Monte Carlo simulations and gives equivalent results with variational Gutzwiller method [44][45][46][47][48][49][50][51][52].…”