Cooperative ring exchange and the fractional quantum Hall effect

Abstract

We study the transition of the interacting two-dimensional electron gas at high magnetic field from a low-density Wigner crystal to a higher-density correlated state which exhibits the fractionally quantized Hall effect. The phase transition is precipitated by a condensation of ring-exchange processes, which by nature of their sensitivity to enclosed magnetic flux allow for especially low-energy exchange condensates at certain values of the Landau-level filling factor, ν=${\nu }_i$. In the condensate, the exchanges mediate a logarithmic potential between local-density fluctuations, leading to a cusp in the ground-state energy as a function of ‖ν-${\nu }_i$‖ in the vicinity of a preferred state. In addition, we derive quasiparticle excitations of sharp fractional charge which are analogous to the excitations derived by Laughlin.