Magnetism of iron and nickel from rotationally invariant Hirsch-Fye quantum Monte Carlo calculations

TL;DR

This paper introduces a rotationally invariant quantum Monte Carlo method for studying magnetic properties of iron and nickel, providing accurate Curie temperatures and insights into the effects of Coulomb interaction approximations.

Contribution

The authors develop a novel rotationally invariant Hirsch-Fye quantum Monte Carlo algorithm that improves magnetic property calculations in correlated electron systems.

Findings

Results agree with continuous-time quantum Monte Carlo benchmarks.

Curie temperatures match experimental values.

Density-density Coulomb interaction overestimates magnetic transition temperatures.

Abstract

We present a rotationally invariant Hirsch-Fye quantum Monte Carlo algorithm in which the spin rotational invariance of Hund's exchange is approximated by averaging over all possible directions of the spin quantization axis. We employ this technique to perform benchmark calculations for the two- and three-band Hubbard models on the infinite-dimensional Bethe lattice. Our results agree quantitatively well with those obtained using the continuous-time quantum Monte Carlo method with rotationally invariant Coulomb interaction. The proposed approach is employed to compute the electronic and magnetic properties of paramagnetic $\alpha$ iron and nickel. The obtained Curie temperatures agree well with experiment. Our results indicate that the magnetic transition temperature is significantly overestimated by using the density-density type of Coulomb interaction.