Ferromagnetism in one-dimensional metals: breakdown of the Hartree-Fock approximation and possible first order phase transition

TL;DR

This paper investigates ferromagnetism in one-dimensional metals, revealing that electron interactions lead to non-analytic corrections in the Gibbs potential, which suggest a first-order quantum phase transition.

Contribution

It demonstrates that second-order electron interactions cause non-analytic behavior in the Gibbs potential, indicating a first-order transition in 1D metals.

Findings

Non-analytic corrections in Gamma(M) proportional to M^2 ln|M| and |M|^3

First-order paramagnetic-ferromagnetic quantum phase transition in 1D metals

Breakdown of the Hartree-Fock approximation in this context

Abstract

We calculate the Gibbs potential Gamma (M) of a one-dimensional metal at constant magnetization M to second order in the screened electron-electron interaction U. At zero temperature we find that Gamma (M) contains non-analytic corrections proportional to M^2 \ln | M| and | M |^3, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order.