Magnetism in the single-band Hubbard model

TL;DR

This paper applies a spectral density approach to the Hubbard model to analyze spontaneous magnetic ordering, revealing phase transition types and the impact of non-local self-energy on quasiparticle properties.

Contribution

It introduces a self-consistent spectral density method with a two-pole ansatz to study magnetism in the Hubbard model, including non-local self-energy effects.

Findings

Identification of conditions for spontaneous ferromagnetism and antiferromagnetism.

Discovery of second order phase transitions away from half filling.

Analysis of non-local self-energy effects on quasiparticle band narrowing.

Abstract

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. Starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch-bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second order phase transitions are found away from half filling, but close to half filling the system exhibits a tendency towards first order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (Tc, Tn) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.