Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario

TL;DR

This paper develops simplified effective Hamiltonians for frustrated quantum Heisenberg antiferromagnets at high magnetic fields, enabling detailed analysis of their low-temperature thermodynamic properties and revealing phenomena like BKT transitions.

Contribution

It introduces a localized-magnon based approach combined with strong-coupling perturbation theory to improve analysis of frustrated spin systems beyond flat-band scenarios.

Findings

Effective Hamiltonians accurately describe low-energy properties.

Identification of a BKT phase transition in the 2D model.

Observation of steep entropy increase and low-temperature specific heat peaks.

Abstract

We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory we also use a localized-magnon based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model.