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

TL;DR

This paper investigates the temperature-dependent magnetic susceptibility of one-dimensional interacting electrons, revealing unique low-temperature behavior due to marginal operators and comparing theoretical predictions with Monte Carlo simulations.

Contribution

It provides a detailed analysis of the spin susceptibility in 1D electron systems, highlighting the effects of marginal operators and lattice effects, and compares different computational approaches.

Findings

Susceptibility approaches zero with infinite slope at low T

Non-logarithmic terms are significant at higher T

Effective interaction captures key diagram contributions

Abstract

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reaveals that the Luttinger liquid spin susceptibility $\chi (T) $ 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.