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

TL;DR

This paper investigates quantum entanglement in the Kugel-Khomskii model using exact diagonalization, analyzing how external fields influence entanglement and phase diagrams in finite chains.

Contribution

It provides a detailed analysis of entanglement measures and phase diagrams in the Kugel-Khomskii model, highlighting the effects of external fields on entanglement regions.

Findings

External fields can both enhance and weaken entanglement.

Phase diagrams show regions of nonzero entanglement.

Concurrence effectively measures quantum entanglement.

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.