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Journal of Physics Condensed Matter

Probing quantum discord in a Heisenberg dimer compound

Tanmoy Chakraborty, Harkirat Singh, Sourabh Singh, Radha Krishna Gopal, Chiranjib Mitra

Published Sep 25, 2013• 6 citations
Publisher

Abstract

A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrating the specific heat versus temperature data. Subsequently, quantum discord, total correlations and spin-spin correlation function are quantified from susceptibility and internal energy and plotted as a function of temperature. Violation of Bell's inequality is also tested for NH4CuPO4, H2O via both experimental susceptibility and specific heat data signifying the presence of entanglement.

DOI
10.1088/0953-8984/25/42/425601

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A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrating the specific heat versus temperature data. Subsequently, quantum discord, total correlations and spin-spin correlation function are quantified from susceptibility and internal energy and plotted as a function of temperature. Violation of Bell's inequality is also tested for NH4CuPO4, H2O via both experimental susceptibility and specific heat data signifying the presence of entanglement.
Entangled solid state systems have gained a great deal of attention due to their fruitful applications in modern quantum technologies. Herein, detection of entanglement content from experimental magnetic susceptibility and specific heat data is reported for NH4CuPO4·H2O in its solid state crystalline form. NH4CuPO4·H2O is a prototype of Heisenberg spin 1/2 dimer system. Temperature dependent magnetic susceptibility and specific data are fitted to an isolated dimer model and the exchange coupling constant is determined. Field dependent magnetization isotherms taken at different temperatures are plotted in a three dimensional plot. Subsequently, entanglement is detected both from susceptibility and specific heat through two different entanglement measures; entanglement witness and entanglement of formation. The temperature evolution of entanglement is studied and the critical temperature is determined up to which entanglement exists. Temperature dependent nature of entanglement extracted from susceptibility and specific heat shows good consistency with each other. Moreover, the field dependent entanglement is also investigated.
The total quantum correlation (discord) in Heisenberg dimers is expressed via the spin-spin correlation function, internal energy, specific heat, or magnetic susceptibility. This allows one to indirectly measure the discord through neutron scattering, as well as calorimetric or magnetometric experiments. Using the available experimental data, we found the discord for a number of binuclear Heisenberg substances with both antiferromagnetic and ferromagnetic interactions. For the dimerized antiferromagnet copper nitrate $\mathrm{Cu}({\mathrm{NO}}_{3}){}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2.5{\mathrm{H}}_{2}\mathrm{O}$, the three independent experimental methods named above lead to a discord of approximately 0.2--0.3 bit/dimer at a temperature of 4 K. We also determined the temperature behavior of discord for hydrated and anhydrous copper acetates, as well as for the ferromagnetic binuclear copper acetate complex $[{\mathrm{Cu}}_{2}\mathrm{L}(\mathrm{OAc})]\ifmmode\cdot\else\textperiodcentered\fi{}6{\mathrm{H}}_{2}\mathrm{O}$, where L is a ligand.
Violation of Bell’s inequality test has been established as an efficient tool to determine the presence of entanglement in quantum spin 1/2 magnets. Herein, macroscopic thermodynamic quantities, namely, magnetic susceptibility and specific heat have been employed to perform Bell’s inequality test for [NH4CuPO4, H2O], a spin 1/2 antiferromagnet with nearest neighbor interactions. The mean value of the Bell operator is quantified and plotted as a function of temperature. The threshold temperature is determined above which the Bell’s inequality is not violated and a good consistency is found between the analyses done on magnetic and thermal data.
An experimental quantification of concurrence and quantum discord from heat capacity (Cp) measurement performed over a solid state system has been reported. In this work, thermodynamic measurements were performed on copper nitrate (CN, Cu(NO3)2⋅2.5H2O) single crystals which is an alternating antiferromagnet Heisenberg spin 1/2 system. CN being a weak dimerized antiferromagnet is an ideal system to investigate correlations between spins. The theoretical expressions were used to obtain concurrence and quantum discord curves as a function of temperature from heat capacity data of a real macroscopic system, CN.
The characterization of quantum information quantifiers has attracted a considerable attention of the scientific community, since they are a useful tool to verify the presence of quantum correlations in a quantum system. In this context, in the present work we show a theoretical study of some quantifiers, such as entanglement witness, entanglement of formation, Bell’s inequality violation and geometric quantum discord as a function of the diffractive properties of neutron scattering. We provide one path toward identifying the presence of quantum correlations and quantum nonlocality in a molecular magnet as a Heisenberg spin-[Formula: see text] dimer, by diffractive properties typically obtained via neutron scattering experiments.
We demonstrate that inelastic neutron scattering technique can be used to indirectly detect and measure the macroscopic quantum correlations quantified by both entanglement and discord in a quantum magnetic material, VODPO4 . 1D2O. The amount of quantum correlations is obtained 2 by analyzing the neutron scattering data of magnetic excitations in isolated V4+ spin dimers. Our quantitative analysis shows that the critical temperature of this material can reach as high as Tc = 82.5 K, where quantum entanglement drops to zero. Significantly, quantum discord can even survive at Tc = 300 K and may be used in room temperature quantum devices. Taking into account the spin-orbit (SO) coupling, we also predict theoretically that entanglement can be significantly enhanced and the critical temperature Tc increases with the strength of spin-orbit coupling.