Eur. Phys. J. B 12, 351-365 (1999)
https://doi.org/10.1007/s100510051016

Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

¹ Département de physique et Centre de recherche en physique du solide, Université de Sherbrooke, Sherbrooke, Quebec, Canada J1K 2R1
² Institut canadien de recherches avancées, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
³ 2100 Valencia Dr. apt. 406, Northbrook, IL 60062, U.S.A.

Corresponding author: ^a cbourbon@physique.usherb.ca

Received: 2 March 1999
Published online: 15 December 1999

Abstract

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given.