No abstract

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $(R) is generalized for the case of nonspherical Fermi surfaces. In general $(R) is found to fall off as l/R, s and to oscillate with a period corresponding to a calipering of the Fermi surface in the R direction. For the special cases of parallel or cylindrical regions of the Fermi surface, a slower fallofl of <1>(R) (l/i£ and 1/R 2 , respectively) is obtained. The general expression for the Fourier transform <£ (q) is also considered and displays Kohn anomalies whose form depends on the shape of the Fermi surface in the vicinity of calipering pairs of points. The usual infinite slope in # (q) for the spherical Fermi surfaces changes in the more general case and becomes a discontinuous slope for a "waist" and a logarithmic singularity in (q) for parallel regions of the Fermi surface. A number of possible applications of the results are discussed.

What is commonly called the Gutzwiller wave function ip , an approximate ground state of the single-band Hubbard Hamiltonian, is considered here for JV-site N-electron rings, when the number D of doubly occupied sites is small (N = 6, 10, 14, 18). For D-*0 spin correlations in ij) surprisingly close to the exact values at zero bandwidth are found (i.e., those of the antiferromagnetic Heisenberg-model ground state). But the energy is grossly in error. A simple modification of ip reproduces the exact energy with remarkable accuracy. PACS numbers: 75.10.Jm, 75.10.LpThe single-parameter correlated-electron ground state due to Gutzwiller, 1 and appropriate to the single-band Hubbard model, 1 ' 2 is a)Here