Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases

摘要

We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chainand determine their fate in the presence of a Raman induced spin-orbit couplingwhich has been achieved in ultracold atomic gases; this system is described bya quantum spin-1 chain with a spiral magnetic field. The spiral magnetic fieldinitially induces helical order with either ferromagnetic or dimer orderparameters, giving rise to a spiral paramagnet at large field. The spiralferromagnet-to-paramagnet phase transition is in a novel universality class,with critical exponents associated with the divergence of the correlationlength $\nu \approx 2/3$ and the order parameter susceptibility $\gamma \approx1/2$. We solve the effective spin model exactly using the density matrixrenormalization group, and compare with both a large-$S$ classical solution anda phenomenological Landau theory. We discuss how these exotic bosonic magneticphases can be produced and probed in ultracold atomic experiments in opticallattices.