A high-temperature expansion method for calculating paramagnetic exchange interactions

TL;DR

The paper introduces a high-temperature expansion method to calculate isotropic exchange interactions in the paramagnetic phase by mapping spin correlations onto the Hubbard model, providing a transparent and effective approach.

Contribution

It presents a novel high-temperature expansion technique for exchange interactions based on mapping spin correlations onto the Hubbard Hamiltonian, with validation against eigenvalue spectra.

Findings

The method yields accurate exchange interactions compared to spectral data.

Application to quantum rings demonstrates the method's effectiveness.

Different Hubbard spectrum parts contribute variably to exchange interactions.

Abstract

The method for calculating the isotropic exchange interactions in the paramagnetic phase is proposed. It is based on the mapping of the high-temperature expansion of the spin-spin correlation function calculated for the Heisenberg model onto Hubbard Hamiltonian one. The resulting expression for the exchange interaction has a compact and transparent formulation. The quality of the calculated exchange interactions is estimated by comparing the eigenvalue spectra of the Heisenberg model and low-energy magnetic part of the Hubbard model. By the example of quantum rings with different hopping setups we analyze the contributions from the different part of the Hubbard model spectrum to the resulting exchange interaction.