Nonlocal Exchange Interactions in Strongly Correlated Electron Systems

TL;DR

This paper investigates how nonlocal ferromagnetic exchange influences strongly correlated electrons using an advanced variational method, revealing continuous phase transitions unlike the abrupt changes predicted by mean field theory.

Contribution

It extends a correlated variational scheme to explicitly include symmetry-broken phases and applies it to the $SU(2)$-Hubbard-Heisenberg model, providing new insights into phase transition nature.

Findings

The variational approach predicts continuous phase transitions.

Mean field theory predicts discontinuous transitions.

Phase diagram shows competition between ferromagnetic and antiferromagnetic correlations.

Abstract

We study the influence of ferromagnetic nonlocal exchange on correlated electrons in terms of a $SU(2)$-Hubbard-Heisenberg model and address the interplay of on-site interaction induced local moment formation and the competition of ferromagnetic direct and antiferromagnetic kinetic exchange interactions. In order to simulate thermodynamic properties of the system in a way that largely accounts for the on-site interaction driven correlations in the system, we advance the correlated variational scheme introduced in [M. Sch\"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for explicitily symmetry broken electronic phases by introducing an auxiliary magnetic field. After benchmarking the method against exact solutions of a finite system, we study the $SU(2)$-Hubbard-Heisenberg model on a square lattice. We obtain the $U$-$J$ finite temperature phase diagram of a $SU(2)$-Hubbard-Heisenberg model within the correlated variational approach and compare to static mean field theory. While the generalized variational principle and static mean field theory yield transitions from dominant ferromagnetic to antiferromagnetic correlations in similar regions of the phase diagram, we find that the nature of the associated phase tranistions differs between the two approaches. The fluctuations accounted for in the generalized variational approach render the transitions continuous, while static mean field theory predicts discontinuous transitions between ferro- and antiferromagnetically ordered states.