Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids

TL;DR

This paper investigates how quasiholes in anisotropic fractional quantum Hall liquids behave in static and dynamic scenarios, revealing their shape, intrinsic geometry, and evolution after sudden parameter changes.

Contribution

It introduces a microscopic analysis linking quasihole anisotropy to the system's intrinsic metric and explores their real-time dynamics post-quench.

Findings

Quasihole anisotropy correlates with the intrinsic metric in static systems.

Quasihole shape evolution reflects the postquench intrinsic metric.

Quasihole dynamics are associated with a spin-2 quadrupole mode.

Abstract

We present a microscopic study of quasiholes in bosonic fractional quantum Hall (FQH) liquids at filling factor $\nu=1/2$ 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 FQH 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 FQH system.