In this talk, we study the system of strongly interacting spinor bosons or fermions in a square lattice subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC). We map out its global phase diagram which displays rich and novel quantum phases and phase transitions in the whole 2 dimensional SOC parameter space. They include masses generated from "order from quantum disorder" mechanism, collinear spin-orbital coupled magnetic phase, quantum commensurate (C) and In-commensurate (IC) non-coplanar Skyrmion crystal phases, stripe co-planar (spiral) C and IC phases, quantum Lifshitz C-IC transitions, metastable states, hysteresis, topological rational and irrational winding numbers,  incomplete and complete devil staircases, Cantor sets, multi-fractals, etc. Various perspectives and possible intimate connections with topological spin liquids or quantum spin glass  are discussed. Implications on current or near future cold atom systems and on so called Kitaev materials with SOC are discussed.

叶锦武教授本科就读于清华大学, 后赴美留学获得耶鲁大学理论物理博士学位, 随后在哈佛大学开展博士后研究工作。现任首都师范大学长江学者教授和美国密西西比州立大学教授。他的主要研究领域是强相互作用的电子、玻色子、自旋、光子等的合作现象和量子或拓扑相变理论。