Magnetic susceptibility of a one-dimensional Fermi system and dielectric function of a two-dimensional Coulomb gas

Abstract

A relation between the magnetic susceptibilityχ(k, ω) of an interacting 1-D Fermi system and the dielectric functionε(q) of a 2-D Coulomb gas is established. By applying a cluster-expansion technique and by using known results for the pair-correlation function of the Coulomb gas we obtain a number of expressions forε(q) which apply in different regions of theq-plane and in different temperature intervals. These results supplement the existing picture of the transition from non-metallic to metallic behaviour occurring in the 2-D Coulomb gas as the temperature increases. The relation betweenε(q) andχ(k, ω) is then used to derive explicit expressions forχ(k, ω) from these results forε(q). The change in the dielectric response of the 2-D Coulomb gas is reflected by a change in the magnetic response of the 1-D Fermi system: as a function of the spin non-flip coupling constantγ _∥ the susceptibility of the Fermi system changes from normal paramagnetic behaviour to non-magnetic behaviour characteristic of a bound singlet-spin ground state, asγ _∥ decreases. Our result for the gap in the spin excitation spectrum of the Fermi system is in agreement with the results of other authors.