A colorful approach to the fractional quantum Hall effect
Résumé
The different types of fractional quantum Hall effect may be described in terms of multi-color quantum liquids. This is the result of a trial wave function approach which yields a complementary vision of the fractional quantum Hall effect. Indeed, each color group of two-dimensional particles in a strong magnetic field forms a Laughlin liquid. However, in a typical system, there is only one type of particles, say gray, and the colors need to be viewed as an artificial marking. In order to get rid of these artificial colors, we have proposed a procedure which renders all particles gray again. This may be viewed as taking a black-and-white photo of a colorful painting. Amazingly, the black-and-white photo reveals an internal structure of the quantum liquid - it consists of distinct droplets the number of particles of which is that of the original colors. The performed numerical calculations indicate that this structure may be a common feature of the different types of fractional quantum Hall states, such as the composite-fermion states or else the 5/2 state with its exotic excitations.