Breakup of a Stoner model for the 2D ferromagnetic quantum critical point

Re-interpretation of the results by [A. V. Chubukov et. al., Phys. Rev. Lett. 90, 077002 (2003)] leads to the conclusion that ferromagnetic quantum critical point (FQCP) cannot be described by a Stoner model because of a strong interplay between the paramagnetic fluctuations and the Cooper channel, at least in two dimensions.Comment: 5 pages, 2 EPS figures, RevTeX

Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases

Using the bosonization approach we study fermionic systems with a nonlinear dispersion relation in dimension d>2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent state path integral technique we built up the effective action that governs the dynamics of the Fermi surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters. In particular we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.Comment: RevTeX4, 9 pages, 2 eps figures, Final version as appeared in Phys.Rev.

The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.Comment: 25 pages, RevTeX 3.

Effective Interaction Potentials in the Uppermost Landau Level

We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume that the lower Landau levels are full and inert causing no Landau level mixing. While it is known that the problem of electrons interacting with the Coulomb interaction in a higher Landau level is mathematically equivalent to the problem of electrons in the lowest Landau level interacting with an effective interaction, the way the effective interaction can be calculated is not unique. We focus on the details of two different calculations of such effective interaction potentials in the uppermost Landau level and discuss the influence of one or another form of the effective potential on the stability of various correlated electronic phases in the quantum Hall regime