An important part of Laughlin’s famous theory of the fractional quantum Hall effect is that his proposed wave-function is an exact ground state for a toy hamiltonian with short range interactions and translation invariance.
An equally important part of the theory is that the proposed wave-function should be robust against various forms of perturbations: lowering the filling factor slightly, including trapping/impurity potentials, taking the long range part of the interaction into account …
I shall discuss mathematical results motivated by these expectations. The problem at hand is to minimize the perturbations within the (large !) class of states that exactly minimize the toy hamiltonian. Our main result is that it is sufficient (in the large particle number limit) to generate uncorrelated quasi-holes on top of Laughlin’s wave function.
Joint works with Elliott Lieb, Alessandro Olgiati and Jakob Yngvason.
Coffee and pastries at 11h00.
LPMMC – UMR 5493 CNRS et Université Grenoble-Alpes