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

TL;DR

This paper uses the Jordan-Wigner transformation to analyze the magnetic properties of the quantum spin-1/2 XX diamond chain, comparing approximate fermionic methods with exact diagonalization results.

Contribution

It introduces a gauge-invariant fermionic approach to study the XX diamond chain's magnetic behavior, including interaction effects and temperature dependence.

Findings

Magnetization exhibits a 1/3 plateau and a jump at intermediate fields.

Approximate methods agree well with exact diagonalization for finite chains.

Temperature effects influence the magnetic phase transitions.

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.