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arXiv:1204.5669 · Physics Letters A

Quantification of entanglement from magnetic susceptibility for a Heisenberg spin 1/2 system

Tanmoy Chakraborty, Harkirat Singh, Diptaranjan Das, Tamal K. Sen, Chiranjib Mitra

Published Sep 1, 2012• 14 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2012.08.051

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Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.
We study the macroscopic entanglement properties of a low-dimensional quantum spin system by investigating its magnetic properties at low temperatures and high magnetic fields. The spin system chosen for this is copper nitrate (Cu(NO 3 ) 2 × 2.5H 2 O), which is a spin chain that exhibits dimerization. The temperature and magnetic field dependence of entanglement from the susceptibility and magnetization data are given, by comparing the experimental results with the theoretical estimates. Extraction of entanglement has been made possible through the macroscopic witness operator, magnetic susceptibility. An explicit comparison of the experimental extraction of entanglement with theoretical estimates is provided. It was found that theory and experiments match over a wide range of temperatures and fields. The spin system studied exhibits quantum phase transition (QPT) at low temperatures when the magnetic field is swept through a critical value. We show explicitly for the first time, using tools used in quantum information processing, that QPT can be captured experimentally using quantum complementary observables, which clearly delineate entangled states from separable ones across the QPT. We have also estimated the partial information sharing in this system from our magnetization and susceptibility data. The complementarity relation has been experimentally verified to hold in this system.
We have established a quantum antiferromagnetic Heisenberg-Ising model on a spin-1/2 pyrochlore edge-shared ladder with Heisenberg intra-rung and Ising inter-rung interactions as a perspicuous candidate to exhibit magnetization mid and zero plateaus, characteristic peaks of magnetic susceptibility, and thermal entanglement mid plateau. The model is exactly solvable and thus, all the essential properties such as the thermal entanglement and the magnetic properties of the system can be exactly calculated. The calculations are done both through the transfer matrix technique and through the reduced density matrix. The magnetization plateaus are observed at zero and half the saturation value and the magnetic susceptibility exhibits a clear demonstration of the associated characteristic peaks. The model also displays the mid plateau of the thermal entanglement as a function of the external magnetic field at low temperatures.