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The Jordan-Wigner transformation is applied to study magnetic properties ofthe quantum spin-1/2 $XX$ model on the diamond chain. Generally, theHamiltonian of this quantum spin system can be represented in terms of spinlessfermions in the presence of a gauge field and different gauge-invariant ways ofassigning the spin-fermion transformation are considered. Additionally, weanalyze general properties of a free-fermion chain, where all gauge terms areneglected and discuss their relevance for the quantum spin system. Aconsideration of interaction terms in the fermionic Hamiltonian rests upon theHartree-Fock procedure after fixing the appropriate gauge. Finally, we discussthe magnetic properties of this quantum spin model at zero as well as non-zerotemperatures and analyze the validity of the approximation used through acomparison with the results of the exact diagonalization method for finite (upto 36 spins) chains. Besides the $m=1/3$ plateau the most prominent feature ofthe magnetization curve is a jump at intermediate field present for certainvalues of the frustrating vertical bond.

Magnetic properties of the quantum spin-1/2 XX diamond chain: The Jordan-Wigner approach