There exists many quantum or topological phases in nature. The well known organization principle of these phases is through various quantum or topological phases transitions between or among these phases. Here, we report they could also be also organized through either complete or in-complete devil staircases. We show that both classes of organization principle appear in an experimentally accessible system: strongly interacting spinor bosons or fermions subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC) in the space of the two SOC parameters $ ( \alpha, \beta) $ in a square lattice. We argue that there is no third organization principle. Contrasts to quantum spin liquid (QSL) phases with topological orders due to geometric frustrations and QSL with quantum chaos due to quenched disorders in Sachdev-Ye-Kitaev (SYK) models are made. Implications on un-conventional magnetic ordered phases detected in the 4d- or 5d-orbital strongly correlated Kitaev materials with SOC and in the current or near future cold atom systems are presented. This talk is pedagogical, should be accessible to any graduate students.
Venue: TDLI Meeting Room 200
Here is the Zoom link if you prefer to join us remotely:
https://zoom.com.cn/j/92869508894
Password:843515