Renormalization group study of a Fragile Fermi liquid in 1+ϵ dimensions

We present a calculation of the low energy Greens function of interacting fermions in 1+ϵ dimensions using the method of extended poor man's scaling, developed here. We compute the wave function renormalization Z(ω) and also the decay rate near the Fermi energy. Despite the lack of ω2 damping characteristic of 3-dimensional Fermi liquids, we show that quasiparticles do exist in 1+ϵ dimensions, in the sense that the quasiparticle weight Z is finite and that the damping rate is smaller than the energy. We explicitly compute the crossover from this behavior to a 1-dimensional type Tomonaga-Luttinger liquid behavior at higher energies.