# Synopsis: A coincidence of errors

#### Critical exponent for the quantum Hall transition

Keith Slevin and Tomi Ohtsuki

Published July 9, 2009

One of the most studied problems in the last twenty years is the integer quantum Hall effect, which describes the response of electrons confined in two-dimensions to a strong perpendicular magnetic field: The electrons move in circular orbits that fill bands, called Landau levels, and the Hall conductance (i.e., the conductance perpendicular to an induced current) of the electrons is quantized.

Like any phase transition, the change of the Hall conductance between quantized values (as the electrons are moved between Landau levels by an external voltage or magnetic field) can be described by a critical exponent, $\nu$. Both numerical calculations and experiment agree fairly well about the value of $\nu$. But as Keith Slevin at Osaka University and Tomi Ohtsuki at Sophia University, both in Japan, argue in a Rapid Communication appearing in Physical Review B, this may be because of a coincidence of errors. Namely, numerical calculations have so far ignored Coulomb interactions between electrons, which should in fact be important, while the experimentally measured value of $\nu$ is based on approximations.

To support their point, Slevin and Ohtsuki have done a new numerical calculation of $\nu$ that gives a value of 2.593, considerably larger than both the currently accepted experimental and theoretical values of ~ 2.37. Their findings will certainly motivate new theoretical models to account for electron-electron interactions in quantum Hall systems. – Jessica Thomas