Linear and non-linear edge dynamics of trapped fractional quantum Hall droplets
Alberto Nardin (University of Trento)
Hybrid: onsite seminar + zoom.
Meeting ID: 956 9527 1626
We study the dynamics of the edge modes of non-harmonically confined macroscopic droplets of fractional quantum Hall fluids, excited by applying some external time-dependent potential to an incompressible ground state belonging to the prominent Laughlin’s series. The neutral edge excitations have been characterized by restricting the Hamiltonian to a suitably truncated subspace of Laughlin-like states, where the the relevant transition matrix elements can be evaluated by Monte Carlo techniques. In the long-wavelength and weak excitation limit we recover observable consequences of the fractional transverse conductivity. The first non-universal corrections to the chiral Luttinger liquid model are then characterized: for weak excitations in the linear response regime, cubic corrections to the dispersion of linear waves and a broadening of the dynamical structure factor of the edge excitations are identified. Sizeable nonlinear effects are found in the dynamics for stronger excitations or on longer timescales. All the observed features are quantitatively captured by a simple nonlinear extension of the standard chiral Luttinger liquid quantum Hamiltonian, whose edge-density evolution equation reduces to a driven Korteweg-de Vries equation in the semiclassical limit.