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

Abstract

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 found solutions provide a possibility to address the problem of quantum entanglement inherent to 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 as 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 on the regions with entanglement, could both enhance and weaken the entanglement depending on the parameters of the models. I.

The resistance of quantum entanglement to temperature in the Kugel-Khomskii model

“…However, this does not occur for all values of the interaction parameters. A significant effect of applied fields in controlling the entanglement has also been demonstrated [34]. It should be mentioned here that since the nature of the model variables can be quite different, the applied fields can also differ: from magnetic (in transition metal compounds) and electric (in optical traps) to elastic stress fields.…”

The resistance of quantum entanglement to temperature in the Kugel-Khomskii model

“…However, this does not occur for all values of the interaction parameters. A significant effect of applied fields in controlling the entanglement has also been demonstrated [30]. It should be mentioned here that since the nature of the model variables can be quite different, the applied fields can also differ: from magnetic (in transition metal compounds) and electric (in optical traps) to elastic stress fields.…”

“…1(a) and 1(b) (see also the discussion concerning the case for T = 0 in Ref. 30). Nevertheless, all the effects, considered in the previous subsection, also manifest themselves here.…”

“…However, in the most physically interesting range of parameters (all the exchange integrals J, I, K and temperature T are of the same order of magnitude) entanglement is not suppressed. Moreover, even at T = 0 the applied field can lead to an increase in the entanglement [30]. For nonzero temperatures, the behavior of entanglement can be also counterintuitive in some cases.…”

“…The ground state has been analyzed for different variants of the Kugel-Khomskii model symmetrical SU(2) × SU(2) [30][31][32], SU(2) × XY [33], SU(2) × XXZ [34], and other related models [35][36][37][38][39].…”