Disorder-driven Phase Transitions In Fractional Quantum Hall Liquids

The fractional quantum Hall state formed in two-dimensional electron gas under strong perpendicular magnetic field is a typical topological order and the only one realized experimentally.The weak disorder in experimental samples is quite important to explain fractional quantum Hall effect,while strong disorder will inevitably destroy the fractional quantum Hall state.As the strength of disorder increases from weak to strong,does something interesting happen in between?In addition,a single impurity can localize the quasihole of the fractional quantum Hall system.What is the relationship between its spatial shape and the geometric degrees of freedom recently proposed in the fractional quantum Hall state?This paper mainly introduces two works I completed based on these problems during my Ph.D.:(1)We present a microscopic study of quasiholes in bosonic fractional quantum Hall liquids at filling factor v=1/2 in the lowest Landau level with anisotropic band mass tensors.We use the spatial density profile to characterize the shape of a quasihole and analyze its anisotropy.We then compare the quasihole’s anisotropy with the intrinsic geometric metric of the system that is extracted from the maximal overlap between the numerically obtained quasihole ground state and a set of model wave functions of anisotropic quasiholes.For a static system,we find that the quasihole’s anisotropy,similar to the intrinsic metric,grows with the anisotropy of the band mass tensor.When the quasihole develops well,we observe a correspondence between the anisotropy of the quasihole and the intrinsic metric of the underlying anisotropic fractional quantum Hall state.We also drive the system out of equilibrium by suddenly changing the band mass tensor.In this case,the shape of the quasihole evolves with time and shows similar dynamics with the intrinsic metric of the postquench state.The evolving frequency matches the energy of a spin-2 quadrupole degree of freedom in the system.Our results suggest that the density profile of a quasihole is a useful tool to estimate the intrinsic metric and capture the dynamics of an fractional quantum Hall system.(2)We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors v=1/2 and v=1 in the lowest Landau level.We use the evolution of ground-state entanglement entropy,fidelity susceptibility,and Hall conductance with increasing disorder strength to identify the underlying phase transitions.The critical disorder strengths obtained from these different quantities are consistent with each other,validating the reliability of our numerical calculations based on exact diagonalization.At v=1/2,we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase.At v=1,we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase,although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the v=5/2 fermionic cousin.