Microscopic Theory of Quasiparticle Spin Fluctuations in a Fermi Liquid.

E. R. Tuttle

Sudhakar Yarlagadda, Gabriele F. Giuliani

We present the microscopic derivation of a quasiparticle pseudo-Hamiltonian for an infinitesimally polarized electron liquid. The Hamiltonian is expressed in terms of suitably defined quasiparticle operators. Our approach is based on a canonical transformation which allows one to replace the bare Coulombic coupling between the interacting electrons with an effective interaction between quasiparticles in which collective charge and spin fluctuations are explicitly accounted for. The relevant matrix elements of the charge and spin-density operators enter our theory via linear-response functions: the charge response, the longitudinal and transverse spin responses, and the mixed charge-spin response. These susceptibilities are in turn expressed in terms of the appropriate many-body local fields. As a consequence our method can be seen as an attempt to satisfactorily include in a self-consistent manner the effects of the vertex corrections associated with charge and spin-fluctuations of the electron liquid. As a result useful expressions for the quasiparticle energy and the effective interaction between two quasiparticles are determined. These can, in turn, be employed in a microscopic determination of the parameters of the Landau theory of the Fermi liquid. The generalization of our results to a multicomponent system is also discussed.

Timo H. Virtanen

Ziqiang Wang

New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.

Arkady Shekhter, Chandra Mohan Varma

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi surface is proportional to the energy measured from the chemical potential, ${\ensuremath{\tau}}_{i}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\epsilon}$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional Fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.

P. J. Hirschfeld