Frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in a magnetic field

TL;DR

This paper develops an effective model for a frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in strong magnetic fields, using exact solutions and numerical methods, with potential relevance to azurite compounds.

Contribution

It introduces a strong-coupling effective description of the frustrated diamond-chain $XXZ$ model in high magnetic fields, simplifying analysis via exactly solvable $XY$ chains.

Findings

Effective spin-1/2 $XY$ chain models accurately describe low-temperature, high-field behavior.

Exact diagonalization confirms the validity of the effective models.

Results are relevant for understanding the magnetic properties of azurite.

Abstract

We consider the antiferromagnetic spin-1/2 $XXZ$ Heisenberg model on a frustrated diamond-chain lattice in a $z$- or $x$-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 $XY$ chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound.