Quantum Monte Carlo study for multiorbital systems with preserved spin and orbital rotational symmetries

TL;DR

This paper introduces a quantum Monte Carlo algorithm that preserves spin and orbital symmetries in multiorbital systems, enabling more accurate studies of Hund's coupling effects in models and real materials.

Contribution

It combines Trotter decomposition and series expansion to treat Hund's exchange terms while maintaining symmetries, improving upon conventional QMC methods.

Findings

Preservation of SU(2) symmetry affects Curie temperature estimates.

The method accurately captures spectral functions of Sr₂RuO₄.

Symmetry preservation prevents overestimation of magnetic transition temperatures.

Abstract

We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exchange is important, where the Curie temperature is grossly overestimated when the symmetry is degraded, as is often done, to Ising (Z$_2$). We then calculate the $t_{2g}$ spectral functions of Sr$_2$RuO$_4$ by a three-band DMFT calculation with tight-binding parameters taken from the local density approximation with proper rotational symmetry.