Dancing Pattern of Electrons in FQH States

a java simulation by Xiao-Gang Wen

• "Flt" describes the strength of quantum fluctuations of the electrons in the quantum Hall state. Flt=0 means no fluctuations (filling factor "nu"=0). "+Flt/-Flt" buttons adjust the strength of the fluctuations.
• "+Ele/-Ele" changes the number of the electrons.
• "In/Out" buttons zoom-in or zoom-out.
• "+Spd/-Spd" buttons control the speed. Simulation is more accurate at small speeds.

This program simulates the motion of electrons in a quantum Hall (QH) state (in the first Landau level). When "Flt"=0, the program simulates a filling fraction "nu"=0 state. Electrons in the "nu"=0 state form a crystal. As "Flt" increases, the quantum fluctuations increase, and program simulates a quantum hall state with a larger filling fraction "nu". When electrons start to exchange places, it means that the crystal state melt into a quantum liquid state due to quantum fluctuations. (When N=7, the melting appear at about Flt=15.) The dancing pattern (the correlated motions) of electrons in the quantum liquid states characterize different quantum Hall states. When "Flt" is too large, the fluctuations are too strong for the simulation to represent the electron motion in any real quantum Hall states.

When there are seven electrons, the following table lists the rough correspondence between "Flt" and filling fractions "nu"

Seven Electrons