Strong-coupling expansion for the spin-1 Bose-Hubbard model

Abstract

In this study, we perform a strong-coupling expansion up to third order of the hopping parameter t for the spin-1 Bose-Hubbard model with antiferromagnetic interaction. As expected from previous studies, the Mott insulator phase is considerably more stable against the superfluid phase when filling with an even number of bosons than when filling with an odd number of bosons. The phaseboundary curves are consistent with the perturbative mean-field theory in the limit of infinite dimensions. The critical value of the hopping parameter t C at the peak of the Mott lobe depends on the antiferromagnetic interaction. This result indicates the reliability of the strong-coupling expansion when U 2 possesses large (intermediate) values for Mott lobe with an even (odd) number of bosons. Moreover, in order to improve our results, we apply a few extrapolation methods up to infinite order in t. The fitting results of the phase-boundary curves agree better with those of the perturbative mean-field approximation. In addition, the linear fit error of t C is very small for the strong antiferromagnetic interaction. * tkimura@kanagawa-u.ac.jp

Ultracold bosons with short-range interaction in regular optical lattices

“…This method works very well for J/U below the critical point (J/U ) c , which is less than one in all dimensions, where all physical quantities are analytical functions. It was used in the studies of spinless bosons with local [51][52][53][54][250][251][252][253][254][255][256][257][258][259] and nearest-neighbor interactions [260,261], two-species bosons [262], and spin-1 bosons [263,264] in different types of regular lattices like hypercubic isotropic [51,52,54,255,[260][261][262][263]265] and anisotropic [253], superlattices [254,255], two-dimensional triangular and kagome lattices [256][257][258], and in the presence of artificial gauge fields [259,265], as well as in disordered lattices [52,67,[266][267][268]. The strong-coupling expansion allows to avoid finite-size effects and shows excellent agreement with exact numerical data.…”

Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices

“…Solving the above quadratic equation (29) and plugging in the culmulant result (27), finally we obtain the following phase boundary equation …”

Superfluid–Mott-insulator transition of spin-1 bosons in optical resonators

“…On the other hand, the spin-dependent collision interactions allow for the population exchange among hyperfine spin states. Rich physics have been disclosed in this system, such as the novel phases [4,5], superfluid-Mottinsulator (MI) transition [6,7], ferromagnetism [8], and spin waves [9].…”

“…Following Ref. [7] of the one-dimensional spin-1 BH model, we take U 2 /U 0 ≈ 0.3 in our calculation.…”

“…The system phase diagram can be mapped out via strong-coupling expansion [7,16]. This is performed by first assuming that the system is in the MI phase with n = n 1 + n 0 + n −1 particles per site and determining the ground-state energy E M (n), then by defining the defect states by adding a particle or hole into the MI state, whose ground-state energy is E ± (n).…”