Strongly correlated magnetic phases of the spin orbit coupled spin-1 Bose-Hubbard chain

Motivated by the ability to engineer artificial gauge fields in ultra cold atomic gases we consider the strong coupling phases of the one-dimensional spin-1 Bose-Hubbard model in the presence of a spin orbit coupling. We determine the low energy magnetic Hamiltonian that describes the bosonic Mott insulating phases with an odd integer filling, which is a spin-1 ferromagnetic bilinear-biquadratic model in a spiral magnetic field. We solve the effective spin Hamiltonian using the density matrix renormalization group and determine the zero temperature quantum phase diagram.