Bose-Einstein condensation of spinor S=1 bosons*

The nature of the BEC transition of S=1 spinor bosons is addressed by Monte Carlo Simulations of the field model [1] of three-component Bose field characterized by O(6) symmetry, with the ferromagnetic interaction g_F breaking the symmetry down to O(3)xU(1) on 3-dimensional cubic lattice. This model is relevant to the condensation of ⁸⁷Rb, ³⁹K and ²³Na ultracold atoms. Worm Algorithm [2] is adapted to the system to calculate one-particle as well as two-particle correlators, including the interconversion rule when a pair of particles with opposite spins transforms into a pair of atoms with zero spin projection each (and vice versa). At g_F=0 the BEC transition is consistent with the O(6) universality class. Using the numerical flowgram method [3], it is shown that at small g_F the criticality flows away from the O(6) universality as the system size increases. The universality of the resulting stable fixed point will be discussed. We also find the tricritcal point g_F=g_T above which the transition becomes discontinuous.
[1] Tin-Lun Ho, PRL 81, 742 (1998);
[2] N. Prokof'ev and B. Svistunov, PRL 87, 160601 (2001);
[3] A.B. Kuklov, N.V. Prokof’ev, B.V. Svistunov, M. Troyer, Ann. Phys., 321, 1602 (2006).