https://doi.org/10.1140/epjb/e2011-10681-5
Magnetic properties of the quantum spin-
XX diamond chain:
the Jordan-Wigner approach
1
Institute for Condensed Matter Physics,
National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011 Lviv, Ukraine
2
Department of Theoretical Physics and Astrophysics, Institute of Physics, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic
3
Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany
Corresponding author: a werch@icmp.lviv.ua
Received:
6
September
2010
Revised:
28
February
2011
Published online:
30
March
2011
The Jordan-Wigner transformation is applied to study magnetic properties of
the quantum spin- 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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011
