Dynamics of quasiholes and quasiparticles at the edges of small lattices

Abstract

We study quench dynamics of bosonic fractional quantum Hall systems in small lattices with cylindrical boundary conditions and low particle density. The states studied have quasiholes or quasiparticles relative to the bosonic Laughlin state at half filling. Pinning potentials are placed at edge sites (or sites close to the edges) and are then turned off. Because the edges of fractional quantum Hall systems host chiral edge modes, we expect chiral dynamics, with motion in one direction for positive potentials pinning quasiholes, and motion in the other direction for negative potentials pinning quasiparticles. We numerically show that chiral motion of the density distribution is observed and robust for the case with positive potentials (quasiholes), but that there is no noticeable chiral motion for negative potentials (quasiparticles). The comparison of the numerical ground states with model lattice Laughlin wavefunctions suggests that both positive and negative potentials do create and pin anyons that are not necessarily well-separated on small lattices. Initializing the dynamics with the model state also shows the lack of chiral dynamics of quasiparticles. Our results suggest that, in small lattices with low particle density, quasiparticles are strongly adversely affected in dynamical processes, whereas quasiholes are dynamically robust.