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

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

2010-04-06

arxiv.org/abs/1004.0848v4

Eur. Phys. J. B80:433-444, 2011

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, 9 figures, accepted for publication in Eur. Phys. J. B

Scientific paper

10.1140/epjb/e2011-10681-5

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-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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