📝 SummarXiv

Abstract

We study phase transitions in bilayer and trilayer bosonic quantum Hall systems. In the absence of interlayer tunneling and interaction, each layer is chosen to have filling factor $\nu=1/2$ or $1$ to realize the Laughlin state or the Moore-Read state. By tuning interlayer tunneling and/or interaction, multiple phases can be generated. In the absence of interlayer interaction, three phase transitions appear when interlayer tunneling becomes sufficiently strong: (1) from two decoupled $\nu=1/2$ Laughlin states to the Moore-Read state in bilayer systems; (2) from one $\nu=1/2$ Laughlin state plus one $\nu=1$ Moore-Read state to the Read-Rezayi $\mathbb{Z}_{3}$ state in bilayer systems; (3) from three decoupled $\nu=1/2$ Laughlin states to the Read-Rezayi $\mathbb{Z}_{3}$ state in trilayer systems. Numerical calculations suggest that these transitions are third-order ones. We propose non-Abelian Chern-Simons-Higgs theory to describe them. If both interlayer tunneling and interaction are present, one-component or multi-component composite fermion liquids and Jain states can be realized. This leads to intricate phase diagrams that host multiple phase transitions and possibly exotic critical points.