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The entanglement is one of the  key features of the  quantum mechanics, that can be exploited for teleportation of quantum states. In this respect many solid state systems (e.g quantum dot) can be used quantum information processors. However, solid state modeling many-body systems is often calculation very difficult, so the approximation is used. In this work, the calculation of entanglement of  ground state of many-body systems by density functional theory  has been performed . For this purpose , first  the charge electronic density, has been calculated  than  the entanglement  has been  investigated by the linear entropy calculation. The investigated systems is the  Hooke’s atom is the system and after calculating the electric charge density of the system for different frequencies, we obtained of change entanglement system with frequency .The results indicated that with decreasing the frequency  in the  Hooke's atom model ,the potential was reduced and entanglement was according by also reduced.

Keywords: quantum entanglement, density functional theory, linear entropy, electric charge density

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