Some sum rules for non-Fermi liquids: Applications taking into account themass renormalization factor

Restudying the non-Fermi-liquid one-particle Green functions (NFLGF) we hav e extended the work of Balatsky [Philos. Mag. Lett. 68, 251 (1993)] and Yin and Chakravarty [Int. J. Mod. Phys. B 10, 805 (1996)], among others. We us e the moment approach of Nolting [Z. Phys. 255, 25 (1972)] to compute the u nknown parameters of the NFLGF's in the framework of the Hubbard model. The zeroth-order moment requires that our one-particle Green functions describ e fermionic degrees of freedom. In order to satisfy the first-order sum rul e, a renormalization, gamma not equal 1, of the free-electron mass is calle d for. The second-order sum rule or moment imposes a relation between the n on-Fermi-liquid parameter, alpha, the Coulomb interaction, U, and the frequ ency cutoff, omega(c). We have calculated the effect of the mass renormaliz ation factor, gamma, on some physical quantities, such as (i) the correlate d momentum distribution function, n(c)((k) over right arrow), close to the effective chemical potential, at T=0; (ii) the superconducting critical tem perature, T-c; and (iii) the superconducting critical interaction, lambda(c r), and compared them with analytical results found in the literature. Also , we have calculated the isotope effect, alpha', for non-Fermi-liquid syste ms, which reduces to alpha'=1/2 (the BCS result) when alpha-->0. As a case of non-Fermi-liquid systems, in the Appendix, we have studied two inequival ent coupled Hubbard layers for which we calculate the one-particle spectral functions on the layers and perpendicular to them. We discuss the features which appear due to the shift in the two effective chemical potentials and propose some experiments to detect the features found from our expressions .