Quantum entanglement, local indicators, and the effect of external fields in the Kugel-Khomskii model

Physical Review B: Condensed Matter and Materials Physics. 2020. Vol. 102. No. 15. P. 155125.

Valiullin V. E., Mikheyenkov A. V., Chtchelkatchev N. M., Kugel K.

Using the exact diagonalization technique, we determine the energy spectrum and wave functions for finite
chains described by the two-spin (Kugel-Khomskii) model with different types of intersubsystem exchange
terms. The obtained solutions provide the possibility to address the problem of quantum entanglement inherent
in this class of models. We put the main emphasis on the calculations of the concurrence treated as an
adequate numerical measure of the entanglement. We also analyze the behavior of two-site correlation functions
considered a local indicator of entanglement. We construct the phase diagrams of the models involving the
regions of nonzero entanglement. The pronounced effect of external fields, conjugated to both spin variables in
the regions with entanglement, could both enhance and weaken the entanglement depending on the parameters
of the models.

Keywords: Quantum entanglement, квантовая запутанность, spin-orbital Hamiltonians, Kugel-Khomskii model, спин-орбитальные гамильтонианы, модель Кугеля-Хомского