We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behavior of the third cumulant $C_3$ as a function of applied voltage, temperature, and barrier height. We predict that $C_3$ can be used to measure the fractional charge at temperatures, which are several orders of magnitude higher than those needed to extract the fractional charge from the measurement of the second cumulant. Moreover, we identify the component of $C_3$, which carries the information about the fractional charge.

• Received 23 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.96.216406