Quantum magnetism of bosons with synthetic gauge fields in   one-dimensional optical lattices: a Density Matrix Renormalization Group   study
  In this paper, we provide a comprehensive study of the quantum magnetism in the Mott insulating phases of the 1D Bose-Hubbard model with abelian or non-abelian synthetic gauge fields, using the Density Matrix Renormalization Group (DMRG) method. We focus on the interplay between the synthetic gauge field and the asymmetry of the interactions, which give rise to a very general effective magnetic model: a XYZ model with various Dzyaloshinskii-Moriya (DM) interactions. The properties of the different quantum magnetic phases and phases transitions of this model are investigated. 
Marie Piraud and Zi Cai and Ian P. McCulloch and Ulrich Schollw\"ock
cond-mat.quant-gas