Non-Perturbative Feats in the Physics of Correlated Antiferromagnets

TL;DR

This paper investigates the breakdown of perturbation theory in the antiferromagnetic phase of the Hubbard model, revealing divergences in vertex functions and linking them to physical crossovers and potential phase instabilities.

Contribution

It extends the analysis of perturbation breakdown to symmetry-broken AF phases, identifying vertex divergences and their relation to physical phenomena in correlated electron systems.

Findings

Vertex divergences occur in the AF phase diagram.

AF order reduces but does not eliminate perturbation breakdown.

Link between vertex divergences and the Slater-Heisenberg crossover.

Abstract

In the last decades multifaceted manifestations of the breakdown of the self-consistent perturbation theory have been identified for the many-electron problem. Yet, the investigations have been so far mostly limited to paramagnetic states, where symmetry breaking is not allowed. Here, we extend the analysis to the spontaneously symmetry-broken antiferromagnetic (AF) phase of the repulsive Hubbard model. To this aim, we calculated two-particle quantities using dynamical mean-field theory for the AF-ordered Hubbard model and studied the possible occurrence of divergences of the irreducible vertex functions in the charge and spin sectors. Our calculations pinpoint the divergences in the AF phase diagram, showing that while the onset of AF order mitigates the breakdown of the perturbation expansion, it does not fully prevent it. Moreover, we have been able to link the changes in the dynamical structure of the corresponding generalized susceptibilities to the physical crossover from a weak-coupling (Slater) to a strong-coupling (Heisenberg) antiferromagnet, which takes place as the interaction strength is gradually increased. Finally, we discuss possible physical consequences of the irreducible vertex divergences in triggering phase-separation instabilities within the AF phase and elaborate on the implications of our findings for two-dimensional systems, where the onset of a long-range AF order is prevented by the Mermin-Wagner theorem.