Quantum discord in spin systems with dipole–dipole interaction

Abstract

The behavior of total quantum correlations (discord) in dimers consisting of dipolar-coupled spins 1/2 are studied. We found that the discord $$Q=0$$ at absolute zero temperature. As the temperature $$T$$ increases, the quantum correlations in the system increase at first from zero to its maximum and then decrease to zero according to the asymptotic law $$T^{-2}$$ . It is also shown that in absence of external magnetic field $$B$$ , the classical correlations $$C$$ at $$T\rightarrow 0$$ are, vice versa, maximal. Our calculations predict that in crystalline gypsum $$\hbox {CaSO}_{4}\cdot \hbox {2H}_{2}{\hbox {O}}$$ the value of natural $$(B=0)$$ quantum discord between nuclear spins of hydrogen atoms is maximal at the temperature of 0.644 $$\upmu $$ K, and for 1,2-dichloroethane $$\hbox {H}_{2}$$ ClC– $$\hbox {CH}_{2}{\hbox {Cl}}$$ the discord achieves the largest value at $$T=0.517~\upmu $$ K. In both cases, the discord equals $$Q\approx 0.083$$ bit/dimer what is $$8.3\,\%$$ of its upper limit in two-qubit systems. We estimate also that for gypsum at room temperature $$Q\sim 10^{-18}$$ bit/dimer, and for 1,2-dichloroethane at $$T=90$$ K the discord is $$Q\sim 10^{-17}$$ bit per a dimer.