Quantum Hall effect from soliton equation

TL;DR

This paper demonstrates that the Laughlin function in the quantum Hall effect satisfies a modified Hirota bilinear difference equation, linking quantum phenomena with integrable soliton equations and revealing new solution structures.

Contribution

It establishes a novel connection between the Laughlin wave function and integrable soliton equations, introducing a modified Hirota equation and Bäcklund transformations.

Findings

Laughlin function satisfies a modified Hirota bilinear difference equation.

Vertex operators generate Bäcklund transformations for solutions.

The equation admits soliton solutions beyond the Laughlin function.

Abstract

The Laughlin function of quantum Hall effect is shown to satisfy Hirota's bilinear difference equation with certain coefficients a little different from the KP hierarchy. Vertex operators which constitute blocks of solutions generate a B\"acklund transformation. Besides the Laughlin function, the equation admits soliton solutions.