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.

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

References in corpus (6)

• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Nature of the spin dynamics and 1/3 magnetization plateau in azurite
• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Magnetism and Thermodynamics of Spin-1/2 Heisenberg Diamond Chains in a Magnetic Field
• Dynamics of the Distorted Diamond Chain
• Jordan-Wigner approach to the frustrated spin one-half XXZ chain

Cited by in corpus (6)

• 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 transverse field XY model on the diamond chain
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain