Third-order quantum phase transitions of bosonic non-Abelian fractional quantum Hall states

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.