Low-energy excitation spectra and excitonic condensate state in strong correlated antiferromagnetic systems

Abstract

The strongly correlated antiferromagnetic lattices can be the scenario for different states of matter. The interactions causing the different situations within these systems are the Kondo exchange and the Heisenberg interaction within a localized spin field. In this work, we analyze the low-energy excitation states of such lattices in any dimension, considering these two interactions in an antiferromagnetic insulator background. These states can be obtained from the associations of fermionic states with spin fluctuation waves. Such composite states interact via the two types of exchange, and their locations and ${E}_{\mathbf{k}}$ dispersions allow one to analyze the main features of the system. For certain values of the bandwidth of the noninteracting system $(\ensuremath{\delta})$ and the Kondo coupling parameter $({J}_{0})$, these composite states either are located within the antiferromagnetic gap, this implying a decrease in the insulating character, or can cross the Fermi level and a quantum phase transition can appear. Some denominated Kondo insulators and the normal state of some antiferromagnetic superconductors might be explained within this model. On the other hand, the charged-particle--magnon mixed states based on electrons and holes present attractive interactions and can then produce magnetic excitons. When these magnetic exciton states are located in the insulating gap, they constitute the lowest energy excitation spectra of the system. In an extreme case, the attractive interaction between the partners of these excitons can be the cause of the appearance of a new phase that presents structural similitude with an insulating Bose-Einstein condensate and a thermodynamic behavior similar to that of the BCS states. The special conditions for the appearance of this condensate are analyzed.