Effect of electron-electron interactions on critical exponents near the metal-insulator transition

Abstract

Electron-electron interactions are incorporated into the localization problem by treating them as a perturbation and the following points are shown. (i) If σ ' (n - n _c)^v and v = 1, then the single-particle density of states is given by N(0)∼(n - n _c)^η with eta; = 1. (ii) If Hartree terms dominate the electron-electron interaction, then v = 1/2. (iii) For v = 1/2 N(0) is non-critical, i.e. η = 0. (iv) A possible classification of the critical exponents of N(0) and σ near the localization transition is suggested in terms of the interplay between exchange and Hartree interactions.