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

Abstract

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.

arXiv comment12 pages, 9 figures, accepted for publication in Eur. Phys. J. B

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• Exact spin-cluster ground states in a mixed diamond chain
• Jordan-Wigner approach to dynamic correlations in spin-ladders
• Quantum Phase Transitions in Alternating-Bond Mixed Diamond Chains with Spins 1 and 1/2
• Jordan-Wigner approach to the frustrated spin one-half XXZ chain
• Inversion phenomenon and phase diagram of the $S=1/2$ distorted diamond chain with the $XXZ$ interaction anisotropy
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Cited by in corpus (8)

• Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• Frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in a magnetic field
• Semiquantitative theory for high-field low-temperature properties of a distorted diamond spin chain
• The specific heat and magnetic properties of a spin-1/2 ladder including butterfly-shaped unit blocks
• The transverse field XY model on the diamond chain
• Spin-1/2 Ising-Heisenberg Cairo pentagonal model in the presence of an external magnetic field: Effect of Landé g-factors
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain