Quantum corrections to the Ising interactions in LiYHoF4

TL;DR

This paper derives an effective low-energy Hamiltonian for LiYHoF4, incorporating quantum corrections from dipolar and hyperfine interactions, revealing complex multi-body effects in the dipolar Ising magnet.

Contribution

It introduces a systematic derivation of a quantum-corrected Hamiltonian for LiYHoF4 using a generalized Schrieffer-Wolff transformation, including multi-body interactions.

Findings

Effective Hamiltonian includes transverse fields and multi-body interactions.

Quantum corrections significantly modify the low-energy description.

Numerical estimates of interaction strengths are provided.

Abstract

We systematically derive an effective two-state Hamiltonian for the dipolar Ising magnet LiYHoF4, including quantum corrections which arise from the transverse dipolar and hyperfine interactions. These corrections are derived using a generalised Schrieffer-Wolff transformation to leading order in the small parameters given by the ratio of the interaction energies to the energy of the first excited electronic state of the Holmium ions. The resulting low-energy Hamiltonian involves two-level systems, corresponding to the low-lying electronic states of the Holmiums, which are coupled to one another and to the Holmium nuclei. It differs from that obtained by treating the electronic states of the Holmium as a spin-1/2 with an anisotropic g-factor. It includes effective on-site transverse fields, and both pairwise and three-body interactions among the dipoles and nuclei. We explain the origins of the terms, and give numerical values for their strengths.