On the onset of antiferromagnetism in the Hubbard model

François Brouers, F. Ducastelle, J. Giner

We calculate the response to a periodical external magnetic field of the magnetically disordered phase of the Hubbard model in the alloy analogy approximation. We investigate the behaviour of the q-dependent susceptibility and in particular we look for a possible divergence of the susceptibility for a wave-vector corresponding to an antiferromagnetic ordering. We do not find any instability for a half-filled or nearly half-filled band.

Michael Plischke

G. Z. Wei, H. Q. Nie, K. Y. Zhang

M. Reitner, Lorenzo Del Re, Massimo Capone +1 more

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.

Elizabeth Nowadnick, Steven Johnston, Brian Moritz +2 more

We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two-dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge-density-wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon-mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established and where there are signatures of a possible metallic phase.

Roland Münzner, Adolfo Avella, Ferdinando Mancini