2-DIMENSIONAL ELECTRON LIQUID IN A WEAK MAGNETIC-FIELD

We present an effective theory describing the low-energy properties of an interacting two-dimensional electron gas at large noninteger filli ng factors nu much greater than 1. Assuming that the interaction is su fficiently weak, r(s) < 1, we integrate out all the fast degrees of fr eedom, and derive the effective Hamiltonian acting in the Fock space o f the partially filled Landau level only. This theory enables us to fi nd two energy scales controlling the electron dynamics at energies les s than h omega(c). The first energy scale, (h omega(c)/nu)ln(nu r(s)), appears in the one-electron spectral density as the width of a pseudo gap. The second scale, r(s)h omega(c), is parametrically larger; it ch aracterizes the exchange-enhanced spin splitting and the thermodynamic density of states.