Bipartite entanglement via distance between the states in a one dimensional spin 1/2 dimer copper acetate monohydrate

Abstract

In this paper, we used a theoretical measure known as distance between the states, $\mathcal{E}(\rho_e)$, to determine the bipartite entanglement of a one dimensional magnetic dimer system. The calculation was compared with the well-known entanglement measure, concurrence, and found to be the same. $\mathcal{E}(\rho_e)$ was, then, expressed in terms of two thermodynamic quantities, namely, magnetic susceptibility and specific heat. Experimental verification of temperature variation of the bipartite entanglement measure in terms of magnetic susceptibility and specific heat was done on single crystals of copper acetate-an excellent one dimensional dimer system. The results showed the existence of bipartite entanglement till temperatures as high as room temperature! Large sized single crystals of copper acetate were grown by a new evaporation technique and characterised by TGA, IR and Raman spectroscopy measurements. Density functional theory calculations were done to calculate the delocalisation index which showed much lower values of $\delta(Cu,Cu)$ than other bonds, implying that the probability of direct Cu-Cu exchange in copper acetate is very small. Band structure calculations revealed the presence of flat bands at the Fermi level implying very weak intermolecular interactions in copper acetate.