The Fermi Liquid and the Luttinger Model

G. Benfatto, Giovanni Gallavotti

Alexei M. Tsvelik

We consider conditions for existence of fermionic quasiparticles in a strongly anisotropic quasi-one-dimensional metal. The adopted model is a model of chains of spin-1/2 Luttinger liquid coupled by small interchain hopping. It is shown that the Luttinger liquid becomes more stable with decrease of the lattice coordination number. It is also shown that with a significant spin-charge separation some Luttinger liquid features may persist in the Fermi liquid phase.

Heinz J. Schulz, Gianaurelio Cuniberti, P. Pieri

Oliver J. Curtin, Yunori Nishikawa, Alex C. Hewson +1 more

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral I L , which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of I L with I L = ± π /2, occur in impurity models classified as singular Fermi liquids. Here we show the same values, I L = ± π /2, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.

G. Benfatto

Michael El-Batanouny

Treats non-Fermi liquids and quantum critical points and describes Luttinger liquid theories. Bosonization of the noninteracting and interacting Tomonaga–Luttinger models are derived. Bosonization of the single particle operators is establshed and the corresponding Green functions derived.