Instabilities of the Hubbard chain in a magnetic field

TL;DR

This paper analyzes the instabilities in a Hubbard chain under a magnetic field, revealing how magnetic field influences dominant fluctuations and extends beyond conformal-field theory to include finite-frequency divergences.

Contribution

It provides a detailed characterization of the instabilities and response functions of the Hubbard chain in a magnetic field, including finite-frequency divergences beyond conformal-field theory.

Findings

Instabilities occur at momenta related to Fermi points.

Magnetic field enhances transverse SDW dominance.

Finite-frequency divergences are identified in Green and response functions.

Abstract

We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studing all response functions at low frequency \omega and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) \sigma =\uparrow ,\downarrow Fermi points, \pm k_{F\sigma}. For finite values of the on-site repulsion U the instabilities occur for single \sigma electron adding or removing at momenta \pm k_{F\sigma}, for transverse spin-density wave (SDW) at momenta \pm 2k_F (where 2k_F=k_{F\uparrow}+k_{F\downarrow}), and for charge-density wave (CDW) and SDW at momenta \pm 2k_{F\uparrow} and \pm 2k_{F\downarrow}. While at zero magnetic field removing or adding single electrons is dominant, the presence of that field brings about a dominance for the transverse \pm 2k_F SDW over all the remaining instabilities for a large domain of $U$ and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half filling and in the transverse-spin response function in the fully-polarized ferromagnetic phase.