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

T. Verkholyak (), J. Strečka, M. Jaščur and J. Richter

The European Physical Journal B: Condensed Matter and Complex Systems, 2011, vol. 80, issue 4, 433-444

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Date: 2011
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DOI: 10.1140/epjb/e2011-10681-5

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