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Magnetic properties of the quantum spin-\(\frac{1}{2}\) XX diamond chain: the Jordan-Wigner approach

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Abstract.

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-\(\frac{1}{2}\) XX model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the presence of a gauge field and different gauge-invariant ways of assigning the spin-fermion transformation are considered. Additionally, we analyze general properties of a free-fermion chain, where all gauge terms are neglected and discuss their relevance for the quantum spin system. A consideration of interaction terms in the fermionic Hamiltonian rests upon the Hartree-Fock procedure after fixing the appropriate gauge. Finally, we discuss the magnetic properties of this quantum spin model at zero as well as non-zero temperatures and analyze the validity of the approximation used through a comparison with the results of the exact diagonalization method for finite (up to 36 spins) chains. Besides the m = 1/3 plateau the most prominent feature of the magnetization curve is a jump at intermediate field present for certain values of the frustrating vertical bond.

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Authors and Affiliations

  1. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011, Lviv, Ukraine

    T. Verkholyak

  2. Department of Theoretical Physics and Astrophysics, Institute of Physics, P. J. Šafárik University, Park Angelinum 9, 040 01, Košice, Slovak Republic

    T. Verkholyak, J. Strečka & M. Jaščur

  3. Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, 39016, Magdeburg, Germany

    J. Richter

Authors
  1. T. Verkholyak
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  2. J. Strečka
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  3. M. Jaščur
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  4. J. Richter
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Correspondence to T. Verkholyak.

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Verkholyak, T., Strečka, J., Jaščur, M. et al. Magnetic properties of the quantum spin-\(\frac{1}{2}\) XX diamond chain: the Jordan-Wigner approach. Eur. Phys. J. B 80, 433–444 (2011). https://doi.org/10.1140/epjb/e2011-10681-5

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  • DOI: https://doi.org/10.1140/epjb/e2011-10681-5

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