低维强关联格点体系中人工自旋-轨道耦合效应的理论研究

项目名称： 低维强关联格点体系中人工自旋-轨道耦合效应的理论研究

项目编号： No.11474029

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 赵继泽

作者单位： 北京应用物理与计算数学研究所

项目金额： 80万元

中文摘要： 自旋-轨道耦合起源于狄拉克方程的非相对论近似。这种耦合广泛存在于空间反演不对称的固体材料中，其性质一般很难调控。最近，在中性冷原子和费米子系统中成功实现了可调控的人工自旋-轨道耦合，引起了广泛的研究兴趣。本项目拟运用密度矩阵重整化群、量子蒙特卡洛等数值算法结合平均场来研究在冷原子系统中实现的人工自旋-轨道耦合效应， 特别是在一维和二维光格子中引入自旋-轨道耦合以后出现的新的相以及自旋-轨道耦合对系统的拓扑、输运性质的影响。我们拟研究两分量和多分量Bose(Fermi)-Hubbard等模型中加入自旋-轨道耦合后出现的新相图，以及在势阱中的新奇现象；我们也准备研究这类系统中的元激发，特别是拓扑类型的元激发以及其动力学行为。本申请人在国际上较早研究格点玻色子系统中人工自旋-轨道耦合效应，有希望在相关领域做出一些有一定影响力的理论工作。

中文关键词： 量子相变；自旋轨道耦合；光晶格；密度矩阵重整化群；超流绝缘体转变

英文摘要： Spin-orbit coupling inherited in the nonrelativistic approxiamtion of Dirac equation, is ubiquitious in atoms and solids lack of inversion symmetry. It describes the response of the spin degree of freedom to the orbital degree of freedom. However,in solids the spin-orbit coupling is usually very weak and lack of controllability in experiments. Recently, Lin et.al. engineered synthetic spin-orbit coupling in a neutral atomic Bose-Einstein condensate with a pair of lasers coupling two atomic spin states. This experiment has triggered great interest in both experimentalists and theorists mainly due to its controllability and relevance to some novel effects. In this proposal, we plan to investigate the effect of the synthetic spin-orbit coupling realized recently in cold atomic systems by using density-matrix renormalization group(DMRG), quantum Monte Carlo as well as mean field theory. We mainly focus on the effect of the synthetic spin-orbit coupling on the phase diagrams in lattice models. We intend to study the two-component Bose(Fermi)-Hubbard models with spin-orbit couplings. We expect that we can discover some novel phases and accurately extract the phase boundaries, the critical exponents as well as the universality class of the corresponding phase transitions. We are also interested in the elementary excitations as well as the dynamics of such systems. In particular, we are interested in the topological excitations. Furtherly, we would extend our work to N(N>2)-component systems.

英文关键词： quantum phase transition;spin-orbit coupling;optical lattice;density-matrix renormalization group;superfluid-Mott insulator transition