Coulomb glass in the restricted random phase approximation

A three-dimensional model of N/2 electrons localized on N randomly distributed donor sites of density n and with the acceptor charge uniformly smeared on these sites, -e/2 on each. has been considered in the restricted random phase approximation (RRPA) which uses the set of 3N Fourier components of the local charge density as the independent collective variables. The energy e(T) per site and the density of one-site excitation energy (DOSE) g(epsilon) are shown to he, respectively, in excellent quantitative and in good qualitative agreement with the Monte Carlo simulation data in the whole temperature region 0.1 < T < 100, where these simulations were performed (e(2)n(1/3)/k(B) being the temperature scale). The pair correlator for the one-site energies g(epsilon,+/-epsilon, r) is found to have the slow decoupling law similar to(+/-1/r) for T less than or similar to 1 and r much greater than r(d) (r(d), Debye screening radius). The status of the commonly accepted asymptotic g(epsilon) similar to (epsilon - mu)(d-1) (d and mu being, respectively, the spatial dimension and the Fermi energy) is discussed. The "deduction" of this asymptotic is shown to be based on the strong and questionable conjecture about decoupling of correlations between one-site excitation energies in the vicinity of mu. (C) 2002 Elsevier Science B.V. All rights reserved.