Landau's quasiparticle mapping: Fermi liquid approach and Luttinger liquid behavior

A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasiparticles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the number of quasiparticles is important. The transformation is performed numerically for a one-dimensional system, i.e., the worst case for a Fermi liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an approach may open a route to a unified description of Fermi and Luttinger liquids on all energy scales.