Magnetic properties of the quantum spin-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\frac{1}{2}$</EquationSource> </InlineEquation> XX diamond chain: the Jordan-Wigner approach

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\frac{1}{2}$</EquationSource> </InlineEquation> 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