Quantum discord in spin systems with dipole-dipole interaction

Abstract

The behavior of total purely quantum correlation (discord) in dimers consisting of dipolar-coupled spins 1/2 is studied. We found that the discord Q=0 at the absolute zero temperature. With increasing the temperature $T$, at first the quantum correlations in the system increase, smoothly reach the maximum, and then turn again into zero according to the asymptotic law $T^{-2}$. It is also shown that in absence of external magnetic field $B$, the classical correlation $C$ at $T\to 0$ is, vice versa, maximal. Our calculations predict that in crystalline gypsum $\mathrm{CaS}{\mathrm{O}}_4\cdot 2{\mathrm{H}}_2\mathrm{O}$ the value of natural (B=0) quantum discord between nuclear spins of hydrogen atoms is maximal at the temperature of 0.644 $\mu$K, and for 1,2-dichloroethane ${\mathrm{H}}_2\mathrm{ClC}-\mathrm{C}{\mathrm{H}}_2\mathrm{Cl}$ the discord achieves the largest value at $T=0.517\mu$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.

11 pages, 6 figure