Two classes of organization principle: quantum/topological phase transitions meet complete/in-complete devil staircases and their experimental realizations

TL;DR

This paper explores the coexistence of quantum/topological phase transitions and devil staircase phenomena in a strongly interacting spinor boson system with spin-orbit coupling, revealing new magnetic phases and topological characterizations.

Contribution

It introduces the Rotated Ferromagnetic Heisenberg model and connects quantum phase transitions with devil staircase structures in an experimentally accessible system.

Findings

Identification of a quantum Lifshitz transition in the RFHM.

Introduction of topological winding numbers to characterize devil staircases.

Discovery of fractal and measure properties of phases in the system.

Abstract

There exists many quantum or topological phases in Nature. One well known organization principle is through various quantum or topological phases transitions between or among these phases. Another is through either complete or in-complete devil staircases in their quantized forms. Here, we show that both classes of organization principle appear in an experimentally accessible system: strongly interacting spinor bosons 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. In the strong coupling limit, it leads to a new quantum spin model called Rotated Ferromagnetic Heisenberg model (RFHM). The RFHM leads to rich and unconventional magnetic phases even in a bipartite lattice. For the first class, by identifying a suitable low energy mode, we investigate a new quantum Lifshitz transition from the Y-x to the IC-SkX-y phase. For the second class, we introduce the topological rational and irrational winding numbers $ W $ to characterize the incomplete or complete devil staircases and also perform their quantizations. The IC-YZ-x/LQx phases form a Cantor set with a fractal dimension along the complete devil staircase. They also take most of measures in the incomplete devil staircases when $ \beta \ll \alpha $. Quantum chaos and quantum information scramblings along the diagonal line $ \alpha=\beta $ are discussed. Implications on un-conventional magnetic ordered phases detected in the 4d- or 5d-orbital strongly correlated materials with SOC and in the current or near future cold atom systems are presented.