Abstract
We examine the superfluid-Mott insulator (SF-MI) transition of antiferromagnetically interacting spin-1 bosons trapped in a square or triangular optical lattice. We perform a strong-coupling expansion up to the third order in the transfer integral t between the nearest-neighbor lattices. As expected from previous studies, an MI phase with an even number of bosons is considerably more stable against the SF phase than it is with an odd number of bosons. Results for the triangular lattice are similar to those for the square lattice, which suggests that the lattice geometry does not strongly affect the stability of the MI phase against the SF phase.
Highlights
The development of optical lattice systems based on laser technology has renewed interest in strongly correlated lattice systems
We find that higher-order terms mostly render the SF phase more stable against the MI phase because the area of the MI phase mostly becomes smaller for higher-order expansions, which is similar to the case of spinless Bose–Hubbard model
Comparing the results obtained in the square lattice and those obtained in the triangular lattice, we find that tC is roughly 6/4 = 3/2 times greater in the square lattice than that in the triangular lattice, because of the difference between the number of nearest-neighbor sites z [z = 4(6) in the square lattice]
Summary
The development of optical lattice systems based on laser technology has renewed interest in strongly correlated lattice systems. QMC methods confirmed that conjecture in a two-dimensional (2D) square lattice [8] Another interesting property of the spin-1 Bose–Hubbard model with antiferromagnetic interactions is the first-order phase transition: the SF-MI phase transition is of the first order in a part of the SF-MI phase diagram. For the second-order SF-MI transition, the strong-coupling expansion of kinetic energy [12] is excellent for obtaining the phase boundary This method has been applied to the spinless [12, 13], extended [14], hardcore [15], and two-species models [16], and the results agree well with QMC results [13, 15]. Some long equations that result from the strong-coupling expansion are summarized in Appendix A
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