High-temperature expansion method for calculating paramagnetic 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 the 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 at half-filling with different hopping setups, we analyze contributions from different parts of the Hubbard model spectrum to the resulting exchange interaction. The developed method can be applied for simulating magnetic couplings in correlated materials and surface nanostructures. ©2016 American Physical Society.