Instabilities in Luttinger liquids

TL;DR

This paper investigates magnetic and charge instabilities in perturbed Luttinger liquids, linking them to the vanishing of the effective Fermi velocity and divergence of the Luttinger parameter, with analysis of specific models.

Contribution

It identifies the conditions under which metamagnetism and phase separation occur in Luttinger liquids, providing a theoretical framework for understanding these instabilities.

Findings

Metamagnetism associated with vanishing Fermi velocity in XXZ chain.

Phase separation linked to divergence of Luttinger parameter in Hubbard model.

Qualitative agreement with previous theoretical studies.

Abstract

We discuss the appearance of magnetic and charge instabilities, named respectively metamagnetism (MM) and phase separation (PS), in systems which can be described by a perturbed Luttinger liquid. We argue that such instabilities can be associated with the vanishing of the effective Fermi velocity v, which in some cases coincides with a divergence of the effective Luttinger parameter K. We analyze in particular an XXZ chain with next-nearest-neighbor interactions in different limits where MM shows up and an extended Hubbard model where in turn, PS occurs. Qualitative agreement with previous studies is found.