Conserved quantities of SU(2)-invariant interactions for correlated fermions and the advantages for quantum Monte Carlo simulations

TL;DR

This paper introduces invariants for the SU(2)-symmetric Kanamori Hamiltonian that significantly enhance the efficiency of quantum Monte Carlo simulations for multi-orbital strongly-correlated systems, enabling studies of complex phenomena like orbital-selective Mott transitions.

Contribution

The authors develop a set of invariants for the SU(2)-symmetric Kanamori Hamiltonian that greatly accelerates quantum Monte Carlo calculations for multi-orbital models.

Findings

Invariants enable faster fermionic trace calculations.

Application to systems with up to seven orbitals.

Feasibility of studying orbital-selective Mott transitions.

Abstract

In the context of realistic calculations for strongly-correlated materials with $d$- or $f$-electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the SU(2)-symmetric Kanamori Hamiltonian which allows to massively speed up the calculation of the fermionic trace in hybridization-expansion continuous-time quantum Monte Carlo algorithms. As an application, we show that, exploiting this set of good quantum numbers, the study of the orbital-selective Mott-transition in systems with up to seven correlated orbitals becomes feasible.