Magnetic phase transitions of insulating spin-orbit coupled Bose atoms in one-dimensional optical lattices

Abstract

We consider the insulating spin-orbit coupled Bose atoms confined within one-dimensional optical lattices and explore their ground-state magnetic phase transitions. Under strong interactions, the charge degrees of atoms are frozen and the system can be described by an anisotropic XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction and transverse field. We apply the matrix product state method to obtain low-energy states and analyze the lowest energy gaps and the ground-state magnetization and correlations. We find when the transverse field is absent, the ground state is a gapped ferromagnetic phase with long-range correlation in the z-direction if the interspin s-wave interacting strength is stronger than that of the intraspin one, otherwise it is a gapless Luttinger liquid (LL) phase with algebraic decaying correlation. When the transverse field is turned on, the gapless LL phase is broken, there emerges a long-range correlated phase with ferromagnetic, antiferromagnetic or spiral order, which depends on the DM interaction strength. We believe our study provides a complete understanding of the interplay between SOC and quantum magnetism of spinor atoms in optical lattices.

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

“…The effective super-exchange spin model with the Dzyaloshinskii-Moriya type interaction can be obtained by the second-order perturbation theory [51,52] in the MI regime of two-dimensional (2D) spin-orbit coupled BH model. The spiral, vortex crystal and skyrmion crystal magnetic structures, are found by applying the classical Monte-Carlo (MC) simulations, bosonic dynamical mean-field theory, variational order and tensor network states methods [53][54][55][56][57][58][59][60][61][62][63][64]. The effects of the strength and symmetry of SOC on the SF phase and MI-SF phase transition are also investigated.…”