Quantum liquids in correlated systems

Particular aspects of two different relevant systems in contemporary Condensed Matter Physics are studied: heavy fermion materials and the newly discovered graphene (an atom thick layer of graphite), specifically its bilayer.;On one hand, the physics of heavy fermion materials under strong external magnetic fields is analyzed from a mean field point of view. The evolution of the heavy fermion ground state under the application of a magnetic field is investigated. A richer version of the usual hybridization mean field theory is presented, which allows for hybridization in both the singlet and triplet channels and incorporates a self-consistent Weiss field. It is shown that for a magnetic field strength B☆, at a filling-dependent fraction of the zero-field hybridization gap, the spin up quasiparticle band becomes fully polarized---an event marked by a sudden jump in the magnetic susceptibility. The system exhibits a kind of quantum rigidity in which the susceptibility (and several other physical observables) are insensitive to further increases in field strength. This behavior ends abruptly with the collapse of the hybridization order parameter in a first-order transition to the normal metallic state. It is argued that the feature at B☆ corresponds to the "metamagnetic transition" in YbRh2Si2. These results are in good agreement with recent experimental measurements.;For the case of the graphene bilayer, the effect of electron-electron interactions on the properties of a graphene bilayer is studied within the Hartree-Fock-Thomas-Fermi theory. It is found that the electronic compressibility is rather different from those of either the two-dimensional electron gas or ordinary semiconductors. An inherent competition between the contributions coming from intra-band exchange interactions and inter-band interactions leads to a non-monotonic behavior of the compressibility as a function of carrier density. Also analyzed is the effect of the interactions on the quasiparticle dispersion. It is found that the electronic fluid can be described by a non-interacting-like dispersion but with renormalized parameters. The interacting theory is compared with recent cyclotron resonance experiments in this system. The results suggest that the electronic fluid can be described in terms of an effective Lorentz invariant theory with renormalized mass and velocity, the Dirac liquid.