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Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain

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  • Mzaouali, Zakaria
  • El Baz, Morad

Abstract

A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-12 XX chain. Following the Jordan–Wigner mapping, we diagonalize the hamiltonian of the chain and we check this procedure numerically as well. Using the “Pauli basis expansion” formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity “quantum coherence” where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.

Suggested Citation

  • Mzaouali, Zakaria & El Baz, Morad, 2019. "Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 119-130.
    • Handle: RePEc:eee:phsmap:v:518:y:2019:i:c:p:119-130
    DOI: 10.1016/j.physa.2018.11.062
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    References listed on IDEAS

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    1. Fumani, Fatemeh Khastehdel & Nemati, Somayyeh & Mahdavifar, Saeed & Darooneh, Amir Hosein, 2016. "Magnetic entanglement in spin-1/2 XY chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 256-263.
    2. A. Osterloh & Luigi Amico & G. Falci & Rosario Fazio, 2002. "Scaling of entanglement close to a quantum phase transition," Nature, Nature, vol. 416(6881), pages 608-610, April.
    3. Charles H. Bennett & David P. DiVincenzo, 2000. "Quantum information and computation," Nature, Nature, vol. 404(6775), pages 247-255, March.
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