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 one-dimensional (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: an XYZ model with various Dzyaloshinskii-Moriya (DM) interactions. The properties of the different quantum magnetic phases and phases transitions of this model are investigated.