Theory of spin nematic to spin-Peierls quantum phase transition in ultracold spin-1 atoms in optical lattices

We present a theory of the anisotropy tuned quantum phase transition between spin nematic and spin-Peierls phases in S = 1 systems with significant bi-quadratic exchange interactions. Based on quantum Monte Carlo studies on finite size systems, it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases. The possibility of a weak first order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large-N SO(3N) model for this phase transition and find in the N -> ∞ limit that the transition is generically of first order. Furthermore, we find a critical point in the one-dimensional (1D) limit, where two transition lines, separating spin-nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin-nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for 23Na atoms trapped in an optical lattice, where the nematic to spin-Peierls quantum phase transition naturally arises, are discussed.

Christoph M. Puetter∗  and Michael J. Lawler
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7

Hae-Young Kee†
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 and
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea