The Landau theory predicts spectral weight functions for density and spin-density fluctuations which in the long-wavelength, low-frequency limit should be equal to the true spectral weight functions of a system of interacting fermions. This correspondence plus well-known frequency sum rules provides a means to examine the Landau quasiparticle interaction parameters. Two inequalities are derived:F1 ≥G1 and another relating the first three spin-symmetric Landau coefficients to the radial distribution function and the two-particle potential. We find that the third-moment sum rule is not entirely exhausted by Landau-accountable excitations, and therefore it is the highest order sum rule which can still probe the theory. A third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction. We do not examine this result in detail, but merely conjecture that it may indicate a basic weakness in the Landau theory of spin-density fluctuations.

Emil Safier

Papers

Sum rules and the landau theory of fermi liquids