Nonlinear dynamics at the fractional quantum Hall edge: quantum Korteweg-de Vries equation and solitons
Alberto Nardin (LPTMS)
One of the hallmark features of fractional quantum Hall liquids is the existence of chirally propagating edge modes at their boundary, whose presence has been an invaluable tool for probing the system’s exotic properties, most notably the presence of fractionally charged quasiparticles with anyonic exchange statistics.
The description of these edge modes was pioneered by Xiao Gang Wen already in the early nineties; yet, these systems attract a lot of attention still today. During the talk, I’ll briefly describe how non-linear corrections to Wen’s chiral Luttinger liquid naturally emerge
in anharmonically confined atomic quantum Hall fluids, both in the continuum or on a lattice. These corrections are both dispersive and nonlinear, giving rise to a rich high-energy dynamics beyond Wen.
In particular, the emergent, effective description takes the form of a quantum version of the Korteweg-de Vries
equation, a well-studied fluid-dynamics equation which admits solitonic solutions. I will mostly focus on how this quantum model gives rise to several intriguing new features of the one-dimensional boundary, such as solitons propagating along the system’s boundary and quantum blockaded dynamics leading to the possibility of generating non-classical states of the edge.
I will finally touch on a different aspects of my reaserch at LPTMS: the study of a measurable fractional quantum Hall quasiparticles’ spin, a quantity which is deeply intertwined with their anyonic statistics, and how such a spin is fractionalized between the quasiparticle itself and the system’s edge, leading to its robustness.