Zan Xiaolei, Liu Jing, Han Jinsen, Wu Jianhua, Li Yongqiang
Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China.
Sci Rep. 2018 Jun 14;8(1):9143. doi: 10.1038/s41598-018-27503-0.
Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the m = -1 component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component m = 0 demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.
受近期实验过程的启发，我们系统地研究了在存在外部磁场的情况下，被困在三维光学晶格中的强关联自旋 - 1超冷玻色子。基于最近发展的玻色子动态平均场理论（BDMFT），我们绘制了系统在反铁磁和铁磁相互作用下的完整相图，其中由于自旋相关相互作用和二次塞曼能量的相互作用而发现了各种相。对于反铁磁相互作用，系统表现出竞争磁序，包括向列相、自旋单重态和铁磁绝缘相，这取决于纵向磁化强度；而对于铁磁情况，在小二次塞曼能量下观察到从铁磁到向列绝缘相的转变，并且绝缘相在大塞曼能量下表现出向列序。有趣的是，在低磁场和有限温度下，我们发现强关联超流体存在异常的多步凝聚，即具有反铁磁相互作用的(m = -1)分量的临界凝聚温度随纵向磁化强度增加，而对于铁磁情况，与弱相互作用情况相反，塞曼分量(m = 0)的临界凝聚温度表现出局部最小值。
