Breakdown of the Fermi liquid due to long-range interactions.

Abstract

Fermions interacting via a long-range repulsive potential are considered in [ital D] spatial dimensions, where 1[lt][ital D][le]2. The standard screening picture is found to break down, i.e., the screened effective interaction cannot be treated as instantaneous. For a bare potential which behaves at long distances as [ital r][sup [minus](2[minus][ital D])] [as ln [ital r] in two dimensions (2[ital D])] and within the random-phase approximation, the retardation effects induce an infrared catastrophe that changes the Fermi liquid into a Luttinger liquid in which the occupation number in momentum space is continuous across the Fermi surface. In 2D, the quantum liquid which we investigate may be called a [ital Z]=0 Fermi liquid'' (where [ital Z] is the strength of the quasiparticle pole at the Fermi surface) since the electron propagator has an isolated pole with a constant residue that scales to zero as the size of the system increases to infinity. For 1[lt][ital D][lt]2, the quantum liquid resembles the 1D Luttinger liquid as the single-particle propagator exhibits a branch cut structure. Moreover, we present a ground-state wave function which reproduces the Luttinger-liquid exponent of the momentum distribution near the Fermi surface.