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

We study the odd-integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a universality class with critical exponents associated with the divergence of the correlation length and the order-parameter susceptibility. We solve the effective spin model exactly using the density-matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.043622

*Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases*; J. H. Pixley, W. S. Cole, I. B. Spielman, M. Rizzi, and S. Das Sarma; Phys. Rev. A **96** 043622 (2017). doi:10.1103/PhysRevA.96.043622